The Mariners rejected Peterborough's original offer for the defender, describing it as 'derisory', but Posh director of football Barry Fry has confirmed an increased bid has been submitted and they are awaiting an answer.
"I'm out in Portugal at the moment for the chairman's conference and I have spoken to John Fenty (Grimsby's chairman) and we have upped our original bid," he told skysports.com.
"We are now just waiting to get a response to our improved offer. We love to bring in young and hungry players whom are eager to learn and want to improve themselves at this club, so Bennett does
fit the mould in that sense.
"We are going to try to bring him in, but Grimsby feel they have got an asset in the lad and they don't want him to go cheap, which is fair.
"We have now put in a big bid, which isn't cheap by any means and hopefully we will get our man, but if we don't then we will just move on to other targets."