"I think he would be a great candidate. He has clearly done a good job leading England, he has got the ability to develop relationships with people, and therefore he would be a great candidate for the Lions job," Jones told the BBC.
"He is very good with the players in making sure they understand standards we want in the team, and making sure they understand the values that are important."
Vice captain Billy Vunipola believes Hartley's approach was in accordance with that of Jones, adding that the skipper had the respect of all his team mates.
"I feel he is a clone of Eddie. They are both brutally honest and you have a lot of respect for that because you know where you stand," Vunipola said.
"He will always put the team first. If he thinks you aren't pulling your weight he will tell you, and if you are doing a good job he will tell you. He is very inspirational, and a lot of boys follow him in that respect."
England, who have an unassailable 2-0 lead in the three-test tour of Australia, play the final match of the series in Sydney on Saturday.
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)
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