Jones was the club's player of the year last season
Sunderland striker Kenwyne Jones will undergo exploratory surgery on his injured knee on Monday.
The 23-year-old was injured during Trinidad and Tobago's 3-0 loss to England on 1 June when he collided with England goalkeeper David James.
"Kenwyne's having an operation on Monday and we'll know the exact damage in 24 hours so it's fingers crossed," said Sunderland boss Roy Keane.
"We'll know one way or another so I'll be saying a few prayers."
Sunderland took on Marco van Basten's Ajax side on Sunday at the Stadium of Light, but lost 1-0 with Klaas Jan Huntelaar scoring the only goal of the game nine minutes after the interval.
Speaking last month, Keane said he expected Jones to miss at least two months of the new season.
Jones, who was voted the club's Player of the Year last season, joined Sunderland from Southampton in August 2007 for £6m, scoring eight goals.
Last season was Keane's first full campaign in charge, and he guided the team to 15th place in the Premier League.
As the new season draws closer, he said he was confident the club would continue to progress.
"I'm hopefully a better and wiser manager and I'm confident the team can do better than last year," he said.
"I've learned from my mistakes. We need to keep improving and we've added one or two staff members as we pushed them a lot last year.
"With Kenwyne now being out, Paul McShane's had an operation and (loan signing) Jonny Evans has gone back to Manchester United - we're three players down from a limited squad last year, in terms on numbers."
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