Spurs are set to let captain Michael Dawson walk this summer, and are already lining up replacements for the tough-tackling defender.
O’Shea has emerged as a cut-price target, with his Black Cats contract due to expire in 12 months’ time.
The former Manchester United star was a key member of the North East side’s backline last season, playing a big role as the club hauled themselves clear of relegation and made an appearance at Wembley in the Capital One Cup Final.
Spurs believe that an offer of around £3m will be enough to entice Sunderland to sell, and are sure that the lure of challenging for a top four finish will appeal to the Irish ace.
As well as possessing a wealth of experience, O’Shea can fill in at both right and left-back and has been known to operate in a deep-lying midfield role – which is versatility that may be appealing as Tottenham plan for another season of Europa League action.
Steven Caulker of Cardiff is also seen as an option just a year after he was sold to the Bluebirds.