Peters after an inital struggle last season to make in impact has improved this campaign, and the club believes that the young Canadian could be a possible start of the future. However Town will have to overcome possible work permit issues to keep the midfielder at Portman Road.
Confirming the news to the Official Club Website, Town boss Jim Magilton said: "We are going to hold contract talks with Jaime and his representative next week and offer him a deal.
"Jaime has got better as the season has gone on and has shown us that he has a future here. We think he is going to get even better and deserves a new contract.
"Once everything is sorted out and they are happy we will present our case to the relevant authorities and take it from there."
Meanwhile central defender Ian Miller, who made his debut for the Blues recentley from the bench following succesful loan spells at Darlington and Boston United, is also in line for a new deal.
"Usually I like to put players on a one-year contract to see how they go but Ian has earned the right to have the extra security." Magilton admitted.
"I'm sure he is level-headed and sensible enough to know that he still has a long way to go and a lot to learn and not become complacent.
"Ian has impressed us all with his aptitude and attitude since the moment he walked in the door and again is someone I can see only getting better."
Fabian Wilnis will also be offered a new one year deal with the club, whilst Magilton will be holding further talks with other out of contract players early next week.