However, the Iron Man star says he will only get in touch if her husband Matthew Broderick gives his permission.
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Asked on a visit to New York whether he'd try to contact her, Robert replied: "I'll make a point of trying to see her while I'm here. I'd like to.
"I'll ask (her husband's) permission. I just want to check in for a few minutes. I love Matthew Broderick."
The Hollywood heavyweight, who was the industry's highest paid actor last year, was speaking on Howard Stern's radio show.
Robert and Sarah Jessica dated as teenagers after meeting on the set of Firstborn in 1984. Their relationship floundered as he battled a serious drug problem.
Asked if she broke his heart, he replied: "'I've never been the kind of person to acknowledge what's going on with me at the time, and I'd try to make light of it, but sure, when you're with someone for seven years, 18 to our mid-20s, it's kind of a big deal."
SJP went on to marry Matthew with whom she has three children.
Her ex, meanwhile, has been clean since 2003. He is now happily married to film producer Susan Levin, who is pregnant with their second child together, a baby girl. Robert also has a son Indio from another relationship.
During this week's interview the actor said that if they met, their spouses would be there as well. He even went as far as to invite talk show host Howard along to the big reunion.
"I'd love to have [Matthew] there. I'll bring Susan.
"Would you mind coming just to kind of mediate the whole thing? It would be a natural extension seeing as you're a part of the conversation."