Jones signed a new four-and-a-half-year contract last January after the club rejected Tottenham's advances for the Trinidad & Tobago international, but the arrival of new manager Steve Bruce has raised uncertainty over his future.
Sunderland have offered Portsmouth an initial £11 million for Crouch with another a further £2 million linked to his personal exploits and the club's overall progress under Bruce's stewardship.
The Wearside club are also interested in Tottenham forward Darren Bent and have opened talks with the representatives of Manchester United's Fraizer Campbell which would suggest that Jones could be deemed surplus to requirements this summer at the Stadium of Light.
Bruce will know that Jones - who has been likened to Chelsea striker Didier Drogba due to his all-action style - has prospered in a lone striker's role at Sunderland and last season he struggled to hit it off up front with Djibril Cisse.
Blackburn manager Sam Allardyce is reported to be ready to take advantage of the situation by taking Jones, who was Sunderland's top scorer with 10 goals last season following his recovery from knee surgery, to Ewood Park as a replacement for Roque Santa Cruz.
Tottenham would also be expected to revive their interest in Jones and for their part Sunderland know they will face serious competition for Crouch's services from Aston Villa, Fulham and Blackburn and are unsure about whether he will want to re-locate to the North-East of England.
Should he decide to leave Fratton Park, Crouch, 28, will be badly missed because he scored 16 goals for the club last season but he will want a platform to press his claims for a place in the England squad ahead of the World Cup finals next year.
Huddersfield-born Campbell is also a target for Hull City where he played a key role in the club's promotion to the Premier League during a loan spell from Old Trafford, although a similar arrangement with Spurs last term proved disappointing.
Hull have had a £6 million bid for Campbell, 21, accepted by United but Sunderland will find it easy to match that figure thanks to the largesse of new owner Ellis Short.
Bruce, who has started work in earnest this week at Sunderland following a family holiday in Portugal, is also hoping to be re-united with Wigan's ball-winning midfielder Lee Cattermole.
Manchester City centre-half Richard Dunne is being earmarked as his captain. The out-of-contract Paraguay international centre-back, Paulo Da Silva, 29, has also been offered a deal by Sunderland.