The defender was the subject of two bids from Posh during the summer before signing a new four-year contract at Blundell Park.
Bennett, 19, could join Peterborough in time for their league game at home to Scunthorpe on Saturday and talks regarding a permanent move to London Road will open during the January transfer window.
A statement from Peterborough read: "The club can confirm we are in negotiations with Grimsby Town centre-back Ryan Bennett.
"However, he has not trained with us and a deal will not be finalised on Thursday."
Posh have also announced striker Danny Mills has signed for Rushden & Diamonds for a month and defender Daniel Blanchett has penned a month-long loan deal with Hereford.