The Hoops and Scotland winger, 21, has been plagued with injuries this season and returned from a "nerve problem" for the 4-3 extra-time William Hill Scottish Cup semi-final win over Dundee United at Hampden on Sunday after being out since March 6.
With a view to Celtic's early start in the Champions League next season - the first of three qualifiers for the Parkhead club begin in the middle of July - boss Lennon has said he could give some players a rest after the Clydesdale Bank Premier League title was wrapped up.
That could happen on Sunday against Inverness, if second-placed Motherwell do not hand it to them on a plate by failing to beat Dundee United on Friday night.
Forrest, though, is looking to feature in all five remaining SPL games and the William Hill Scottish Cup final against Hibernian, while hoping to be included in the Scotland squad for the 2014 World Cup qualifier away to Croatia on June 7, as he bids to make up for lost time.
"I don't need a rest, said the former Celtic youth player, speaking at the club's Lennoxtown training complex where he was publicising the visit of Caley.
"I have had my time off being injured so I want to play in all the games. I played on Sunday so I'm hoping to play the remainder of the season.
"Obviously there are only six games left so it is not the best for me but I want to play in as many games as I can. If I am fit (for the Scotland game), I will be available for selection.
"It was nerve problem which was giving me a pain down my leg, which wasn't good. It has been like that since October. But I had an injection on my back to calm things down so hopefully I can play the remainder of the games.
"It was never a major problem, it was niggling but hopefully that's me. It has been frustrating. Hopefully I can get over that and play more next season."
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