The 33-year-old was strongly linked with Spurs during the January transfer window, but eventually joined the Serie A giants on a six-month contract after leaving Bayern Munich.
Tottenham boss Harry Redknapp has since admitted he may have made a mistake in not acting quickly enough to secure the Dutchman’s signature, which has pleased Van Bommel.
“We had some contact with Spurs but unfortunately it didn't work out in the end,” he said to Sky Sports.
"It's one of my favourite clubs in England, I really love the stadium and I know the training ground because I've been there with the Dutch national team.
"Rafael [van der Vaart] has told me a lot of good stories. I'd love to play for Spurs. I've told Rafael that as well.
"I don't know how things will go and that’s all I’d like to say at the moment. I'm pleased with what Harry Redknapp's said about me - that's always positive.
"It's not good to look back. You've got to look to the future. I'm happy at Milan, but you never know what will happen."
The experienced campaigner has already been sent off for Milan since signing for the club, receiving two yellow cards against Catania in his Serie A debut.