The Trinidad & Tobago international has seen his pre-season preparations disrupted after picking up a slight knock.
He has spent much of the last week working with the Black Cats' physios at the club's training camp in Portugal.
Jones was forced to sit out friendlies against Darlington and Portimonense as Steve Bruce's reign at the Stadium of Light began in earnest.
He was, however, able to join up with the rest of the Sunderland squad for a full workout on Wednesday.
The 24-year-old striker is now in contention for the Amsterdam Tournament clashes with Benfica and Atletico Madrid over the weekend.