Allardyce told the club's official website, "We now have three top-class keepers at the club and I don't think there is another Premiership club out there that can compete with us on this level."
"It has been a tough year for Ian, who has found it difficult to oust Jussi Jaaskelainen from the starting line-up.
"I have been impressed with his attitude and commitment and it is very pleasing that he wanted to stay here rather than trying to ply his trade elsewhere."
Meanwhile, Bolton are being linked with Newcastle's Nicky Butt and Cardiff City striker Cameron Jerome.
Jerome, 19, has been a revelation for Cardiff this season and chipped in with 20 goals as the Bluebirds finished just below the play-offs.
A number of clubs including Birmingham City are known to be keen but now Wanderers have entered the running and are said to be weighing up a £3million swoop.