Grimsby chairman described Posh's initial bid for Bennett as "derisory", prompting a second offer last week, but that too was knocked back and Peterborough director of football Barry Fry has confirmed he will no longer pursue the teenage defender.
Fry told the Peterborough Evening Telegraph: "Grimsby contacted me to reject our improved and very reasonable offer, so that's the end of it as far as we're concerned.
"They think they can get a couple of million for the boy, so good luck to them. I'd be amazed if there's anyone out there prepared to match what we offered.
"Bennett is a great prospect, but we will now look elsewhere."