The Frenchman confirmed his desire to remain at Dean Court after he was offered a one-year deal during Friday's end-of-season debriefings with Lee Bradbury and Steve Fletcher.
Out-of-contract this summer, Baudry is expected to agree terms to stay with Cherries when he holds further talks with boss Bradbury today.
And he revealed his primary aim next term would be to reward the club's management duo for backing him by displaying improved performances.
Baudry told the Echo: I am hoping to stay I enjoy it here.
I think I have to give back something to Bradders and Fletch because they have given me confidence. Now, I have to give back something to them.
I think I have more to offer than this season. I was not very fit because I had not played a lot and did not have a lot of reserve games.
I want to come back in pre-season and show I can do more.
Baudry first linked up with Cherries for a trial in January and subsequently signed until the end of the season after his contract with French outfit Troyes had been cancelled by mutual consent.
His first team opportunities were limited by the form of Jason Pearce and Shaun Cooper, as well as a frustrating groin injury.
But Baudry, a product of the Le Havre academy, made a major impact for Bradbury's men when his goal sparked Cherries' crucial comeback win over Bristol Rovers.
A centre-half by trade who can also play in midfield, Baudry also got a taste of the big stage when he returned from injury to come on as a late substitute in the play-off semi-final, second leg defeat at Huddersfield.
Homegrown duo Tim Stephenson and Dan Thomas, as well as Baudry and fellow rookie Ben Williamson are expected to put pen to paper on new deals.
First team star Danny Hollands opted to join Charlton Athletic.