The Northumberland Park development, close to Tottenham's historic White Hart Lane home, would help regenerate one of the most run-down reas of London which was a focal point in riots in August, Johnson said.
However, the club responded with a statement saying it was not yet in a position to commit firmly to the project.
The mayor has offered 8.5 million pounds to persuade the Premier League club to stay in Tottenham and build a new 400 million-pound stadium. A further 8.5 million pounds would come from local Haringey council.
Tottenham have been embroiled in a long-running battle with West Ham United over who should move into the Olympic Stadium in East London once the 2012 Games are over, winning a court hearing for October 18 in an effort to overturn a decision in favour of West Ham.
Most Tottenham fans want the club to stay close to its traditional home. However, the club says that local and national government both have a role to play in supporting the development in area blighted by poverty and unemployment.
"The proposed stadium scheme and wider area development has the potential to lever hundreds of millions of pounds worth of much-needed regenerative development to Tottenham," chairman Daniel Levy said in a statement.
"The overall scheme requires a complex package of financing of which the correct level and nature of public support is critical," he added.
"It would be wholly irresponsible of us to announce we were proceeding with the scheme without the appropriate agreements and support firmly in place. Discussions are continuing with all the relevant stakeholders and we shall, as always, keep our supporters updated."
MAYOR'S FINAL OFFER
The mayor's offer did not come with a definite ultimatum, but he warned no more public money would be put on the table.
If Tottenham do accept, it would help smooth London's bid to host the 2017 athletics World Championships because Tottenham would have taken out the running track from the Olympic Stadium as part of its development of the venue.
"Last month's riots were a telling reminder of just how important it is for Spurs to press ahead with the development at Northumberland Park and to help kick-start a much wider regeneration project that would create jobs and give Tottenham the economic boost it deserves," Johnson said.
The financial package would go on infrastructure and improved transport links around the planned new 56,000-seat stadium in North London.
The club has pursued a new stadium in Tottenham at the same time as bidding to move into the Olympic site.
Plans to develop the North London site were originally approved by the mayor in 2010, but costs resulted in them looking at the Olympic Stadium as an alternative.
Tottenham applied for a judicial review on the Olympic Stadium after losing out to second-tier West Ham, given preferred bidder status by the Olympic Park Legacy Company (OPLC) in February, a decision backed by the mayor and government.
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