Forrester, a 24-year-old attacking midfielder, joined Scottish Championship outfit Rangers from Doncaster Rovers on a six-month loan deal last week.
Kernaghan, a former coach at the Gers who worked with the attacker for two years at Brentford, believes that the key to Forrester’s success in Glasgow will be his fitness.
“There’s no doubt in my mind he’s got what it takes to be a success at a club like Rangers,” the former Republic of Ireland international told The Scottish Sun.
“Harry’s got ability and pace for sure, but he’s also got that strength of character to deal with the pressure of 50,000 fans.
“However, what I would say is that he needs to be proper fit, as fit as he can be in order to get the best out of him. Harry knows that better than anybody.”
Forrester has worked with current Rangers manager Mark Warburton at Watford and Brentford.
The attacking midfielder is a good player and scored one goal in nine appearances for Doncaster this season before moving to the Gers.
The former Aston Villa prospect will be looking to establish himself in the Rangers first team in the coming weeks.
Rangers are at the top of the Scottish Championship table at the moment with 47 points from 19 matches, three points clear of second-placed Falkirk with a game in hand.