The 36-year old Italian defender is out of contract after leaving AC Milan at the end of last season and Impact head coach Jesse Marsch says there is a possibility he could be lured to Saputo Stadium this summer.
"The opportunity to have a guy like Nesta on your team would be a great one and we'd be in a very fortunate position to be able to come to terms with him," said Marsch.
"I'm not sure where it's all going to go as it's complicated. The good part is it's fair to say that Alessandro wants to be here.
"So we're going to figure out what that means and deal with the League and do what we can and see if we can make this happen."