Potential bidders include Richard Desmond's Northern & Shell, News International and the Guardian Media Group.
Desmond, who complained to the Office of Fair Trading about Associated Newspapers' exclusive deal with London Underground in May 2003, is reported to have a freesheet called London-i ready for launch.
News International was ready to launch a free evening paper three years ago but had to scupper plans after its distribution was not comercially viable.
Livingstone will place a notice in the Official Journal of the European Union after Easter, which will allow potential bidders up to three months to complete their offers. A decision is expected by the end of August.
Livingstone made the decision to allow a free afternoon paper to be distributed in Tube stations last year, saying that the exclusive distribution deal with Associated's Metro did not allow Londoners to get the benefit of a free afternoon paper.
Livingstone said today: "For the past six years Associated Newspapers have distributed the Metro in the morning. It's a matter of public record that other newspaper businesses would be willing to distribute a free afternoon paper and might even pay more than we are getting for the Metro deal.
"All newspaper groups will now have a formal opportunity to let us know that they are interested. Any additional money from a new deal would be invested in further improvements to the Tube."
The move could hit the Evening Standard, also part of Associated Newspapers, hard as more of its circulation is eaten away. Its reach in London has been falling over the past few years, falling to 345,776 in February, a drop of 10% year on year. In December last year, Associated launched a free mid-morning version of paper, called Standard Lite, for the centre of London to bolster the paid-for title.
There is no love lost between Livingstone and Associated. The Mayor refused to apologise to the newspaper group in February after a furore concerning a Jewish Evening Standard reporter whom he likened to a "concentration camp guard".
If you have an opinion on this or any other issue raised on Brand Republic join the debate in the .