The Welsh winger is keen to return to the Premier League.
Bale played for Spurs for six years between 2007 and 2013, before leaving for Spain in a then world record fee.
His agents are also speaking to other Premier League teams, but Real Madrid are yet to agree a deal with any club.
Manchester United may turn to Bale if they are unsuccessful in their pursuit of Jadon Sancho, making the likelihood of the 31-year-old returning to play in England more realistic.
Tottenham Hotspur manager, Jose Mourinho, said before the season opener against Everton, which Spurs lost 1-0, that he “needs a striker”.
Mourinho has spent around £30m on the signings of free agent goalkeeper Joe Hart, right-back Matt Doherty from Wolves and midfielder Pierre-Emile Hojbjerg from Southampton this summer, but so far back up for Kane has proved elusive.
