The Chelsea star is so desperate to join the former Blues boss that he will put pen to paper on a four-year, £160,000-a-week deal at the earliest opportunity.
Lampard can sign a pre-contract agreement with the Italian champions on New Year's Day before walking out next June as he is in the last year of his current Chelsea agreement.
One of Lamps' most trusted pals said: "Frank's mind is finally made up once and for all. He wants to team up with Mourinho again as soon as possible.
"Ideally, he would love to go now but Chelsea are saying they will resist all offers and make him see out the final year of his contract.
"Even if Blues eventually crumble and come up with a new five-year deal, I'm sure Frank will tell them where to stick it - the damage is done."