Bodin and Moult have been released by the Lilywhites, with them out of contract at the end of June.
Injuries have restricted them making an impact at North End, 29-year-old Bodin missing the whole of the 2018/19 season with a torn anterior cruciate ligament, while cartilage surgery kept him out for a time in the campaign just finished.
Moult, 28, hasn't kicked a ball in the first-team since August 2019 having also suffered a damaged ACL.
Luton Town boss says best team didn't win after Championship defeat to Preston North End
PNE player ratings vs Luton Town as Ben Whiteman and Liam Lindsay steal the show in hard-fought win
John Smith's PNE Fans' Panel verdict: Sunshine all the way
Longridge Cricket Club will play at Emirates Old Trafford in a bid to win the Lancashire Knockout Cup Final
Match Report: Luton Town 0-1 Preston North End - Brad Potts stunner gives North End first Championship win
He's been back in training since early March and made the bench for two games in April but didn't get on to the pitch.
McAvoy said: "Sometimes people need a fresh start in life. Louis and Billy have been a bit unfortunate with injuries.
"Louis scored against Wigan and then we went to Swansea, he looked great and we were thinking we are going to see the best of him.
"Unfortunately he then suffered that horrific injury. He's now fit and ready to play.
"The unfortunate thing is that in the time he has lost, there are others we have got here who in my opinion are ahead of him at the moment,
"He needs to go and play, he is hungry to go and play football. Billy is similar.
"They need to go and find another home where they can try and flourish as footballers. I wish them all the best and I have the greatest respect for both of them."
Moult scored eight goals in 40 appearances after signing from Motherwell for £450,000 in January 2018.
North End signed Bodin for £500,000 from Bristol Rovers a few days after Moult's arrival. Capped once by Wales, the winger scored four goals in 44 games.
Also being released from the first-team squad are David Nugent, Josh Ginnelly and Graham Burke.
All have been seeing out their contracts on loan - Nugent at Tranmere Rovers, Ginnelly with Scottish club Hearts and Burke in Ireland at Shamrock Rovers.
From the youth-team squad, Kyi Nicholson, Ben Dooley and Harry Huddart have been released at the end of the second year of their scholarships.
Thanks for reading. If you value what we do and are able to support us, a digital subscription is just £1 per month for the first two months. Try us today by clicking here