However, the National Enquirer's report claims Katie Holmes is not on board.
'The word is that Tom is making an effort to be a part of Suri's life again,' an insider snitched.
'He's been planning this for a long time - surprising Suri with gifts and sending her concert tickets and clothes.
'Tom knows that he hasn't been around a lot. He's hoping all this will win Suri over - and it's seems to be working.'
Insiders have revealed that the couple's custody agreement allows Tom to see Suri for ten days each month, but the actor has neglected to use the time, and 'basically turned his back on her.'
The 56-year-old is now attempting to make up the absence ASAP.
'Even though Tom and Suri have been apart for a long time, he's always cared about her,' a friend told the US publication.
'He's realised that he's already missed out on so much with Suri and wants to start using that time. It's his right, and he doesn't see how Katie can try to stop him.'
The National Enquirer's sensational reports adds Katie is worried about Tom's influence on Suri.
'Suri is at an impressionable age, and if Tom becomes a major part of her life, Katie would probably be worried that he'd try and lure her into Scientology.
'If Katie suspects that's the case, she'll do everything she can to stop it.'
'Suri is the most important thing in Katie's life and she's extremely protective of her daughter,' an insider dished. 'Katie's not going down without a fight.
Neither Tom or Katie have responded to the National Enquirer's claims.