24-year-old Otsemobor will be avaliable on a free transfer after turning down an improved contract at Gresty Road.
Otsemobor's agent Erir Walters told the Eastern Daily Press "Jon has had a conversation with the club and we have spoken about the possibility of him joining Norwich," said Walters.
"I would have to say that Norwich are in pole position at the moment. Jon has looked at the set-up there and he was very impressed with the manager and his staff.
"There are other clubs interested including Leeds and Sheffield Wednesday, but Jon is not going to be making any decision until the end of May."
Grant met Otsemobor recenlty at Colney and said that he was exceited at a possible move to Norwich City.
Walters also added "Crewe gave Jon permission to talk to Norwich and he visited the facilities they have got to offer," added Walters. "He was very impressed with the people he met down there - especially manager Peter Grant.
"He has looked at the crowd and the support Norwich regularly get. It is certainly a prospect that interests him a great deal. He sees them as a side with Premiership potential and he would like to get them back to where they belong."