The Brazilian has been the subject of rumours surrounding a shock move across London to join the Blues, with speculation suggesting that a deal may go through before the World Cup later this summer.
Now Real and Milan are also keen on the 25-year-old, and could launch raids even though he only signed for Spurs last year.
Paulinho has struggled to establish himself as a first-team regular at White Hart Lane since his £17m arrival from Corinthians, where he had developed a reputation as one of the world’s most promising midfielders.
Both of the European clubs have been monitoring the South American enforcer for some time, and are confident that they can lure him away from Tottenham as they look set to miss out on Champions League football.
Real would appear to be the more likely side to snap him up, with Los Blancos able to offer him guaranteed top level European action and the chance to follow in the footsteps of some of his compatriots such as Ronaldo and Roberto Carlos.
Milan are also interested as they set to embark on a big summer of transfer activity, while Jose Mourinho is thought to be keen to make the versatile central man a part of his Chelsea squad.