United fan Stam rejected Real
The imposing Dutch international was targeted by several clubs but ended up remaining in Rome, and has managed to find his scoring touch with consecutive goals for the Biancoceleste in the Champions League and Serie A.
"Lazio have said they don't want to let me go," he told World Soccer. "I'm happy with that.
"Once I'd played in the Champions League qualifier, I couldn't play in the competition for anyone else, and that tends to cut out Europe's big clubs. So I set that date as a deadline for myself, and decided that, if Lazio were still my club then, I would stay here for the rest of my contract.
"That runs for another two years, and then I intend to return to Holland and see if a club wants me there.
"I have been abroad for a long time now and I'm keen to play out my career in my own country.
"They (Real Madrid) asked about me, and I like the club, but I want to play another two years, and I don't think they wanted to give me a two-year contract.
"I didn't want to go to another country for one year as my wife is about to have twins and it was too much upheaval."
Stam admits he still has affection for Manchester United, despite being forced out of the club following the publication of his controversial autobiography.
"People keep asking me that (about the autobiography)," he continued. "But, at no time, have I had any regrets.
"When I left, I was happy with the decision I made with my family, and, since then, I have never looked back.
"I still support Manchester United, as I always have, but that chapter of my life is now closed.
"I was surprised David Beckham left Manchester United, but where do you go from there?
"There aren't many better places to go than Real Madrid."