"The British journalist will be released within the next 24 hours," Majid al-Ibadi, who is a judge involved in negotiations with the kidnappers, said.
"The Iraqi translator was released and is in the hands of the security forces."
Following the incident, police in Basra launched an intensive search and cordoned off the Palace Sultan hotel on Tuesday.
The journalist and his interpreter had flown to Basra from Baghdad and checked into the hotel over the weekend.
Hareth al-Athari, head of Shia leader Muqtada al-Sadr's office in Basra, said the interpreter had been taken to a hotel in the city.
He said the kidnappers had become cautious and were delaying the release of the journalist but added that a deal to free him was still in place.
"The kidnappers are cautious. All the indications are positive and we are optimistic. We expect him to arrive any moment. There is no change in the deal."
On Tuesday Sadr's movement distanced itself from the kidnapping, saying it denounced and condemned the abduction of journalists all over Iraq.
Britain's Press Association said the journalist had covered the fall of Baghdad in 2003 and worked for various newspapers including the Sunday Telegraph, the New York Times and the Financial Times.
"It is still early days. We are just praying for him to be safe," it quoted his wife as saying.
At least 208 journalists and media assistants have been killed since US-led forces invaded Iraq in March 2003, according to Paris-based media watchdog Reporters Without Borders.