The Argentinian has fallen behind Karim Benzema in the pecking order at Madrid and has been told that he is free to leave.
According to The People, Higuain would prefer a move to the Premier League, sparking interest from the two rivals.
Arsenal have apparently contacted Madrid already over the transfer, while Spurs may look for the striker to be included in any potential deal for winger Gareth Bale, who has been linked with the Spanish club recently.
The likelihood is that Bale will stay at Spurs for another season, especially if they get into the Champions League, leaving the two London clubs to battle it out over the £22m striker.
It is unknown which club the player himself would prefer to join.