Maddison’s deal at the KCOM Stadium runs out on June 30, but few expect the current campaign to be completed by then.
Hull also have the first option to sign Maddison who is out of contract at the Weston Homes Stadium at the end of the season, but they are not expected to take up that offer.
The terms of his loan deal would make Hull liable to pay Posh a fee if they make the move permanent and his form for the Tigers since joining them in January has not been good.
Posh director of football Barry Fry, the man in charge of transfer dealings at London Road, said: “I’ve spoken to Grant McCann (Hull manager) and told him we would have no objections to Marcus staying at Hull for however long it takes to complete the season.
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“Our manager doesn’t want him here.”
Maddison turned down the chance to move to Championship clubs Charlton and Birmingham City in January in order to become a free agent at the end of the season when he would be expected to secure a better financial package.