Police on Thursday identified the man as Uhnane Daud and said he was not in custody.
They said they had found fingerprints on a plastic bag containing seven detonators found in a van outside a station where the bombers were believed to have boarded the trains.
A police spokeswoman said the Algerian had legal residency in Spain and therefore would have given his fingerprints to authorities when he was applying for it. She said his record showed three past offences under immigration law.
Meanwhile, one of the prime suspects has been charged with belonging to al-Qaida's Spanish cell.
The suspect, Said Berraj, from Morocco, was previously identified by another judge as a central figure in the Madrid train blasts.
Spanish police say their train bombing investigation points to a group of mostly Moroccan Islamists, operating in the name of al-Qaida.
A Spanish judge has accused 19 people, including 15 Moroccans, of involvement in the March 11 bombings.