Hartley missed the June Test series defeat in South Africa due to concussion, but is among the 44 men who will start a three-day training camp on Saturday.
Owen Farrell took over as skipper for a 2-1 series defeat to the Springboks and Jones will wait until a Test against the same opponents in November to decide who will lead the side.
“We are not playing a game so we do not need to decide about captaincy,” the England head coach said.
“We have to make a selection decision for November 3 so when we need to make a selection decision on that we will decide on the captaincy.”
Jones revealed Ashton spoke to him about a potential international comeback before the prolific wing scored a hat-trick for the Barbarians against England in May.
“We had a quick chat,” Jones said. “He had a bit of a glint in his eye which indicated something, and the something was he wanted to come back to England.
“I think he had the idea in his head. He wants to play for England. He sees it as his last opportunity so we are very pleased he has made that decision and we are looking forward to seeing what he can bring to the table.”
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