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Bale flew back to Madrid on Sunday night immediately after signing off his season-long loan from Real with two goals as Spurs beat Leicester 4-2 to book a place in the inaugural Europa Conference League next season.
The 31-year-old is set to spend time with his family, who have remained in the Spanish capital, before joining up with Wales for the European Championship, having said he will not announce his plans until after the tournament.
"I know what I'm doing but it'll just cause chaos if I say anything now," Bale said at the King Power Stadium.
Spurs do not have an automatic option to extend Bale's loan for a further year, nor buy him outright, so they would have to discuss any new arrangement with Real and the forward.
Spurs chairman Daniel Levy personally pushed for Bale's return last summer and is understood to be open to extending his stay in north London, but their new manager would have a say in any fresh approach – with Levy set to accelerate the appointment process now the season is over.
Bale has one year remaining on his Real contract and has no future at the club while Zinedine Zidane is head coach.
Spurs subsidised under half of Bale's reported £500,000-a-week wages for the season and, despite struggling for fitness and often being overlooked by Jose Mourinho, he finished the campaign with 16 goals in total and 11 in the League, where he made only 10 starts.
Bale's late double at Leicester sealed seventh place for Spurs after the visitors had twice cancelled out two Jamie Vardy penalties through Harry Kane and a Kasper Schmeichel own goal.
Kane's goal and pass for Bale's first ensured he is only the second player to finish a Premier League season with the most goals and assists after Andrew Cole in 1993/94.
Kane's representatives are set for talks with Levy now the season has ended, with the striker keen to leave his boyhood club before the start of the Euros.
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