Johnson is currently reviewing the legacy strategy for after the Games and has made no secret that he remains unconvinced of the financial viability of the Stadium being used for athletics post-2012.
He is understood to have preferred a Premiership club like West Ham United or Tottenham Hotspur taking over the stadium afterwards.
But Coe has, reportedly, "leaned on" Johnson to make sure that the promise he made to the International Olympic Committee during the bid that the Games would offer a legacy for athletics will be kept.
The Mayor's office told the Financial Times: "The Mayor has made it clear he wants to see a strong and sustainable legacy for the Olympic Stadium and is working closely with Seb Coe and the 2012 team to ensure that London has a flexible facility that can accommodate athletics as well as other team sports."
An unnamed source told the Financial Times that Johnson was "leaned on" by Coe to stick to the original plan that after the Games the 80,000-seater Olympic Stadium is downsized to a capacity of 25,000 and that League One club Leyton Orient or a Premiership rugby union club have are installed anchor tenants.
Johnson last week announced the formation of a new body to ensure that London is left with a positive regeneration legacy from the 2012 Olympics is to be set-up.
Coe said: "The Mayor is right.
"A new Mayor would want to look at this concept in London terms and I don't think we would disagree wtih that.
"The issue, four years out, for the stakeholders, the Government, the Mayor's office, is what are the structures afterwards, particularly in the Olympic Park, that are going to guarantee that these facilites are going to stay in use?"