Alli has been in excellent form for Tottenham this season as they mounted a title challenge.
Spurs will finish second in the Premier League – ahead of Arsenal for the first time in 25 years – and beat Manchester United yesterday.
But their resolve will be tested by Real who fancy Alli, according to Diario Gol in Spain.
Florentino Perez is already considering his summer overhaul despite being in control of the title race in Spain with two games to play and being in the Champions League final.
And Perez is keen on a new goalkeeper – with David De Gea looking set to join – a new defender, one new superstar striker and another second striker.
Alli is in the running for the second striker role with Kylian Mbappe and Paulo Dybala the options for the new leading man.
Perez wants a player to operate between the lines and link midfield to attack – like Alli does at Spurs.
However Tottenham will not give Alli up easily and would likely quote a similar figure to the £86million they sold Gareth Bale for in 2013.
Tottenham tied Alli down to a six-year contract in September so will be under no pressure to sell unless he pushes for a move.
The England star earns around £50,000-a-week and could be in line for another wage rise this summer to give him parity with the club’s top earners.
Tottenham face a difficult summer with a number of players itching for pay rises and with the move to Wembley for the season.
They waved goodbye to White Hart Lane yesterday by beating Manchester United 2-1.
They will spend next season at Wembley while development of the new stadium continues.
