The likes of Newcastle United are said to be hot on the trail of the 21-year-old this summer.
Jones has enjoyed a terrific season with Peterborough, managing 11 goals and five assists so far.
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The Posh are hoping to hold onto him for as long as possible, but are realistic.
Per the Daily Star, a big offer from the likes of Newcastle would be too hard to refuse.
The Magpies will continue to court young talent as they look to build up their squad within Profit and Sustainability Rules in the Premier League.