The Northampton Saints hooker has been cleared to play rugby again after missing an extended period due to concussion and he has been named in the 44-man England training squad for this weekend's get together.
Hartley had been expected to retain the captaincy of the national side but Jones says that may not be the case, England having struggled during the Six Nations under the forward's leadership.
Owen Farrell stepped in for Hartley for the summer tour of South Africa and although he failed to steer England to a series victory, Jones appears to be giving thought to handing the Saracens back the captaincy on a full-time basis.
"We are not playing a game so we do not need to decide about captaincy," Jones 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 also decided to name wing Chris Ashton in his training squad, despite the 31-year-old having not played international rugby since 2014.
Ashton, who will play for Sale Sharks in the 2018/19 season, scored a hat-trick for the Barbarians against England in May and Jones says he had spoken to the for Saracens man before his man of the match exploits during the summer.
"We had a quick chat," Jones confirmed. "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."