Bennett was named the Mariners' club captain last season.
Grimsby Town chairman John Fenty has confirmed the club has received an improved bid from Peterborough United for 19-year-old defender Ryan Bennett.
Grimsby turned down an offer for skipper Bennett from the newly promoted Championship side last month.
"We have received a substantially improved offer," Fenty confirmed on the club website.
"We are not in a position to respond until I return from the Football League meeting in Portugal."
Fenty also said the Mariners would be looking at any potential interest shown by other clubs but remained adamant they wanted to keep the youngster at Blundell Park.
"I must reaffirm that the club has no desire to sell Ryan - although it is pleasing that other clubs are showing an interest in our players."
Bennett joined Grimsby from Ipswich Town as a trainee and was eventually handed his professional debut in the 2006/07 season.
Voted Young Player of the Year the following season, he later earned a call-up to the England Under-18 squad.
He was then rewarded for his outstanding form at club level when he was handed the captaincy on manager Mike Newell's arrival last season.
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