The 67-year-old resigned as QPR manager earlier this week and is due to undergo replacement surgery on both of his knees.
However, bookmakers are backing Redknapp to make a swift return to the Premier League next season with Newcastle, report the Chronicle.
Indeed, the ex-QPR boss is as low as 6/1 to take over the Magpies and can be found at higher prices with a variety of bookmakers.
The Chronicle suggest Redknapp's links with the Newcastle job are due to owner Mike Ashley's previous attempts to lure him to St James' Park.
John Carver has been announced as Newcastle's full-time boss - but only until next season - and former QPR manager Redknapp is now to free to take the reins as Carver's successor should the job interest him and Ashley indeed want to bring him to Tyneside.
Whether the 67-year-old could work with an owner of Ashley's mould remains to be seen, although his reputation within the game could help him in that respect.
Newcastle host Stoke City on Sunday afternoon, while QPR host Southampton a day earlier at 3pm.