Jack joined Rangers in the summer transfer window after leaving Scottish Premiership rivals Aberdeen at the end of the 2016-17 campaign.
During his time at Aberdeen, the 25-year-old established himself as one of the best defensive midfielders in the Scottish Premiership.
The former Scotland Under-21 international, though, has struggled for his best form at Rangers so far this season.
As reported by The Scottish Sun, Jack has been sent off as many as three times already this season - although two of those dismissals overturned by the SFA.
Former Celtic midfielder Hartley has defended the ex-Aberdeen star and has backed him to eventually come good for Rangers.
Now in charge of Falkirk in the Scottish Championship, the 41-year-old former midfielder, who featured for Rangers’ Old Firm rivals Celtic between 2007 and 2009, played with Hartley at Aberdeen.
“He is a competitor, he loves to win, and he will get stuck in — but he’s not a dirty player,” Hartley told The Scottish Sun about Jack. “Not at all.
“There is nothing nasty about Jacko. He will stand his ground and handle himself, but he’s not a dirty type."
“Ryan has opted for Rangers and clearly wants to get off to a good start — maybe that’s led to him getting involved in things,” added Hartley.
“But how serious has it been? The fact the SFA have reduced two red cards tells you he’s not had much luck during games.
“Maybe sometimes when you go to a new club you are under pressure to impress, but nobody should think Ryan is that type of player.”
Meanwhile, interim Scotland national football team head coach Malky Mackay has explained why he decided to call up Jack for the upcoming international friendly match against the Netherlands.
“Ryan Jack is someone who was Aberdeen captain and was a consistent performer for them and who has gone into Rangers in different circumstances, playing a different style of football and playing with an array of different players,” Mackay told The Glasgow Evening Times.
“Through people I speak to at his own club and previous club and scouts, he is another talented player who we are giving a chance to.”