"We received an offer on Monday. I took it to the board and we turned it down straight away," Scunthorpe manager Alan Knill told BBC Radio Humberside.
"[The offer] was way short of our evaluation, it was less than what we actually paid for him."
O'Connor joined The Iron from Crewe Alexandra in July 2009
for a fee of ?250,000 and has since made 71 appearances for the Lincolnshire club.
Posh's Director of Football, Barry Fry, said they had now turned their attention elsewhere.
He also revealed to BBC Radio Humberside that they are giving a trial to former Iron midfielder Josh Wright.
"We've got Grant McCann and the boy [Josh] Wright playing with us out in Portugal at the minute so we love a Scunthorpe player, don't we?" he said.
The Iron have also lost out on the signing of former Bury loan striker Nicky Ajose who joined Peterborough on a four-year deal on Tuesday.
Source: BBC Sport
Source: BBC Sport