The Muse rocker, who split from the 35-year-old actress last year after four years together, is reportedly eager to rekindle their relationship and even wants them to undergo couple's therapy.
A source said: ''Matt is realising that he misses her and is begging her to give their love and family another try. He's even asked her to go back to counselling with him.''
But the blonde beauty, who has three-year-old son Bingham with the British star, doesn't think they should be together even though she feels bad about ending their engagement.
The insider told Life & Style magazine: ''Although she feels a little conflicted, Kate's ready to move on.''
The 'Something Borrowed' actress, who also has 10-year-old son Ryder with her ex-husband Chris Robinson, is rumoured to have already moved on from Matt with 'Dancing With the Stars' performer Derek Hough, who started giving her dance lessons last year.
The pair surprised everyone when they ''acted like a couple'' at a party in Los Angeles last month.
A source previously said: ''As Kate told Derek about her problems with Matt, they grew closer and closer. Derek knew the relationship was over, so he didn't think twice about hooking up with Kate.''