Virtually ruled out of the series in Australia following the surgery, the 27-year-old pacer said he was hopeful of returning to training in September, thus giving himself a month to prove his fitness.
''There's always a possibility for me to go. I want to push for a place to go on that tour. I've got to work as hard as I can because there is no better feeling than to play against Australia in an Ashes series. That is what's keeping me going,'' he told BBC Sport.
The Glamorgan bowler had a microfracture surgery on his left knee by pioneering surgeon Dr Richard Steadman last month and Jones was advised a three-month rest and England team doctor Peter Gregory admitted Jones' participation in the Ashes was ''extremely unlikely''.
However, the optimism in Jones refuses to give in and he is watching highlights of last year's Ashes victory, in which he played a crucial role with his reverse swing.
''The DVD has been out a few times just to keep me going," said Jones, who will be on crutches for another three weeks.
''It has been hard work these last five weeks and it's only going to get harder, but the rewards will be better if I do get back,'' he said.
Jones missed the winter tour to Pakistan last year with an ankle surgery and then returned from the tour of India after twisting his left knee during practice.
Despite the spate of injuries, Jones warned his critics against writing him off.
''I've got six to seven years ahead of me. I just want to keep going. It's never entered my mind to give up. I just laugh at the people who write me off in the press. I use it as fuel to prove them wrong and make them eat their words,'' he added.