A deal to take Pochettino the Spanish capital in mid-season could be tricky, especially since he only signed a new Tottenham deal in the summer, but Perez is seemingly willing to wait until next summer if Spurs chairman Daniel Levy plays hardball.
Tottenham will visit north London rivals Arsenal in the Carabao Cup quarter-finals after beating West Ham on Wednesday night and Alli, understandably, is looking forward to it.
"That's where the manager might be thinking 'is this now the time for me to step out?' I think Tottenham, if Real Madrid want him, will have a real problem in the next few days". The fans and the club are unbelievable, the players as well, we've got a special bunch of boys and everybody gets on really well. I'll keep working hard every day and keep listening to the manager.
The Colombia international's efforts were hailed by Pochettino, whose team were led by a brace from Son Heung-min.
Alli cited Pochettino, who has coached most of those players to the top of their game, as a main reason for him agreeing to stay, but the Argentinian is keen to stay modest.
"We need to be careful how we manage January", he said. Hopefully the fans will love it.
He said: "We could have got anything".
"I can't think of a better place for a player of my age and where I am in my career, to have such incredible support and coaching staff to help me to keep improving".
Alli said the move to a new home had played "a little part, not a massive part" in his decision to sign a new deal.
"I can't think of a better place for a player of my age and where I am in my career, to have such wonderful support and coaching staff to help me to keep improving". Even in the first half, we were able to have a go.
"When I think about signing, obviously Poch plays a big part in that".