According to the national daily newspaper El Pais on Tuesday, five of the men are still at large, but the sixth, Jamal Zugham is among a group of suspects arrested at the weekend.
Zugham was said to have been recognised by two passengers of one of the trains that was bombed on Thursday morning.
Two hundred people died and nearly 1500 others were wounded when the bombs exploded during morning rush-hour.
El Pais did not give the identity of the other five men who are wanted for questioning.
But police believe that other nationalities could be part of the group that carried out the attacks.
Citing "anti-terrorist" sources the paper said that Jordanian national Abu Musab al-Zarqawi could be the mastermind behind the attacks.
Al-Zarqawi, one of Washington's prime suspects in a string of bomb attacks in Iraq, is suspected of maintaining ties with the al-Qaida network.
A reward for information leading to his capture has recently doubled to $10 million.
Investigators also believe that a video tape in which an unidentified man has claimed responsibility for the train bombings in the name of al-Qaida is authentic, El Pais added.
The video, dropped off in a rubbish bin near a Madrid mosque late on Saturday, featured a man speaking Arabic and confirming his al-Qaida credentials.
He said: "We claim responsibility for what happened in Madrid just two and a half years after the attacks in New York and Washington."