Toure – a three-time Premier League champion – was released by Manchester City earlier this year after eight years at the Etihad.
The Ivory Coast midfielder is now a free agent and could be snapped by some clubs in Europe, with the transfer windows open there.
The Premier League window is closed but Toure is out of contract, so can join a top-flight club as a free agent.
But the player’s agent, Dimitry Seluk, wrote a cryptic message that will leave many fans wondering where his next move will be.
He tweeted: “Toure @YayaToure has passed a medical in London.
He then flat out rejected West Ham as an option, as he tweeted: “It’s not West Ham, 100%.
“Yaya is a champion. The last place is not for him.
“Yaya is close to signing a new contract.”
Tottenham failed to sign a player in the transfer window and could jump at the chance to sign the Ivorian.
Toure’s brother, Kolo, played for Arsenal – another London club who may be open to a move.
But Crystal Palace seem like the club most likely to land Toure.
Before Toure left last season, Pep Guardiola said back in May: “The Brighton we will give him what he deserves, one of the most beautiful experiences a player can receive.
“All the game will be focused on winning and, for Yaya, we are going to try to win it for him.
“We have amazing facilities but we cannot forget the club became higher and higher because of the players.
“Yaya came here at the start of that.
“Where we are in this moment is thanks to what this guy has done.”
Spanish clubs still have time to do business with the window closing on August 31.
However, it is unlikely he will head back to one of his former clubs – Barcelona – anytime soon.
City, meanwhile, drew 1-1 away to Wolves last weekend and host Newcastle on Saturday (5.30pm).