Pedersen is out of contract at the end of the season and has been linked with a move to Turkish side Fenerbahce.
Allardyce replied, when asked if he was confident of keeping Pedersen at the club: “Yeah, I think so.
“We all know he is out of contract this year, so we will have to see what we can do about that.
“There’s no reason for us to do anything with him at this stage, not unless somebody suddenly pops up from abroad to give him a pre-contract.
“If that was the case then we would have heard about that, so we’ll obviously try and continue to talk to him regarding a new contract.”
Pedersen has impressed recently after being moved to a more central position.
“He is getting more of the ball, becoming more active,” Allardyce said.
“He doesn’t have to be quite as quick in that position as he does out wide, so doing that has brought the best out of him.
“It’s been a major bonus for us and him. It’s allowed him to get more involved in the game, to express himself more and he has found more space there.
“He is also finding his quality in the final third, which is something he has done before at this club.
“I hope he continues to grow in confidence like many of the other lads are doing at the moment.
“Some may say it’s a long time over due, but if it’s back, let’s hope it’s back for a long time.”
