The British-born man in his 30s, of Pakistani origin, arrived at a UK port last month and left the country again the day before the attacks, on 7 July, The Times newspaper reported on Thursday.
The suspected bombers were also Britons of Pakistani origin.
According to The Times, security sources say they believe the mastermind was involved with previous "terrorist" operations and had links with followers of Osama bin Laden's al-Qaida group in the United States.
It was believed he had visited the bombers in their home city of Leeds, and also identified targets on the London Underground railway system, where three of the four bombs exploded, the paper said.
Security sources also said he was likely to have trained the recruits in how to trigger their rucksack-carried bombs, three of which went off almost simultaneously at around 8.50am (0750 GMT), at the peak of Thursday morning's rush hour.
Police have reportedly switched their investigation towards seeking the mastermind of the attacks since learning that the four bombers killed themselves in the attacks.
Police want to question a Leeds
University doctorate candidate
According to The Times' Thursday edition, police are also seeking a possible fifth member of the bombers' cell, who was also seen at Luton station, north of London, from where the attackers travelled into the capital.
The man, believed to also be of Pakistani origin, could still be at large in London, the paper said.
Police additionally want to interview an Egyptian-born university lecturer who was in Leeds until a few weeks ago.
According to The Sun newspaper, the man, whom it named as 33-year-old Magdi El-Nashar, was studying for a biochemistry doctorate at Leeds University and disappeared just before the attacks, it is thought to Egypt.
His rented house was one of six addresses in and around the city raided by police on Tuesday morning, the report added.
Late on Wednesday, anti-terrorist police spread their search to the market town of Aylesbury, about 64km northwest of London, searching one residential address but making no arrests and finding no explosives.
The bombers' background became the subject of a row between London and Paris, with Charles Clarke, the British interior minister, denying comments by his French counterpart that British police had arrested some of the suspects in the past.
"It is completely and utterly untrue. I am absolutely staggered he should make that assertion," Clarke told Sky TV.
"I cannot believe it. He wasn't into politics at all, so what drove him to do it? It can't be him, it must be something else behind him"
Bashir Ahmed, uncle of bombing suspect Shehzad Tanweer
He later told Channel Four News, however, that the police and intelligence services were looking at any previous brushes with the law the suspects may have had.
A British police source said it was possible some of the men might have come to the attention of police in the course of normal criminal investigations.
The BBC said two of the suspected bombers had been arrested for minor offences in 2004 and released with a caution - one for disorderly conduct and one for shoplifting.
The BBC also said police were hunting a fifth man, connected to the attackers, but not one of them. The report could not be confirmed by a London police spokeswoman.
Police were granted a warrant enabling them to continue questioning until Saturday a man arrested in West Yorkshire on Tuesday in connection with the attacks.
Police have said four bombers blew up three underground trains and a double-decker bus last Thursday in an attack that officials say bore the hallmark of al-Qaida.
At least three of them came from the Leeds area in northern England, police said. The fourth was believed to be from the same area and a friend of the other three, Sky TV reported, citing a senior security source.
The three men identified by neighbours as the suspects were aged between 19 and 30, members of the sizeable ethnic Pakistani community around the city.
Memorial services have been
taking place across the UK
"They were all British bombers," declared the front page of the Daily Express newspaper, reflecting widespread shock, above a picture of the birth certificate of suspect Shehzad Tanweer.
Friends and family said the 22-year-old Tanweer was a cricket-loving sports science graduate with no interest in politics.
Shock and horror
"I cannot believe it," his uncle, Bashir Ahmed, told reporters. "He wasn't into politics at all, so what drove him to do it? It can't be him, it must be something else behind him."
Irshad Hussain, who has known the Tanweer family for 25 years, said he believed the four had been tricked.
"I believe there was a mastermind behind this who had to kill the four boys because otherwise they would have had evidence. That is the reason they were blown up, because I don't think they realised they were going to be killed," he said.
In Pakistan, an intelligence official said Tanweer had been in the Lahore area from December to February and had stayed at a madrassah or Islamic religious school. Security agencies often point to such schools as breeding grounds for militancy.
The intelligence official, who declined to be identified, said Tanweer was believed to have been the mastermind of the bomb plot, and that the British government had requested information about two of the four men.
Blair said he would look into new
measures to check extremism
The Muslim Council of Britain said it was stunned that those claiming to share its faith seemed to be behind the attacks. "Nothing in Islam can ever justify the evil actions of the bombers," secretary-general Iqbal Sacranie said in a statement.
Prime Minister Tony Blair urged Britain to be tolerant amid fears of a backlash against its 1.6 million Muslims. He said he would look urgently at new measures to tackle extremism, including boosting efforts to stop people entering the country to stir up hatred.
In Brussels, Blair was backed by French Interior Minister Nicolas Sarkozy in calling for tighter European border controls. Sarkozy also said there was a strong suspicion the explosives used in the bombings came from the Balkans or Eastern Europe.
Sarkozy called for EU member states to exchange intelligence on "radical Muslim preachers and imams whose actions disrupt public order by their support for violence, hatred and discrimination", according to his speaking notes.