The Black Cats are not actively looking for buyers for the 29-year-old Benin international, but Press Association Sport understands there is a growing pragmatism on Wearside which dictates that every player has his price.
As a result, the club would have to seriously consider any sizeable bid which came in for any member of their squad, and Sessegnon is one of their most valuable assets and has been linked with a series of potential suitors in recent weeks.
The former Paris St Germain man has been a big hit with fans on Wearside since making his £6million switch to the Stadium of Light in January 2011. At his best, he has terrorised defences, although perhaps not scored the number of goals he might have.
However, inconsistency has been a problem for a player who, despite speculation that he could leave the club last summer, signed a three-year contract extension in August.
There is a feeling on Wearside that Sessegnon has had his head turned by rumours of big-money moves during his time at Sunderland, and he has been linked with Marseille and Chinese sides Tianjin Teda and Shanghai Shenhua already this summer.
Di Canio saw Sessegnon score twice in successive games at the start of his reign, the opener in the 3-0 derby victory at Newcastle and a priceless winner against Everton six days later.
However, he missed the final three games of the campaign through suspension after being rather harshly sent off in a 6-1 defeat at Aston Villa on April 29, a decision the club appealed unsuccessfully.
The new manager is in the process of radically reshaping the playing staff he inherited from predecessor Martin O'Neill, and with owner and chairman Ellis Short determined to get value for money, a different approach has been adopted.
Short invested heavily in Scotland striker Steven Fletcher and England winger Adam Johnson last summer, but this time around, has sanctioned to date a series of moves for lower-profile players with potential.
- Sports & Recreation