The Scotland international has finally put last season's injury problems behind him and returned fully fit for the champions' summer schedule.
Forrest returned to action during the second half of Celtic's 2-1 defeat to CFR Cluj on Saturday but revealed thoughts had already turned to the tie in Belfast next Wednesday.
He told the club's official website: "A few of the boys will train in the build-up and will be ready for that game.
"We're all raring to go in these games, we want to help ourselves get back to fitness as soon as possible and we all want to make a point and stay in the team.
"The trip has been good so far, the games are coming quick and fast so we'll be ready for the Cliftonville game when it comes around. We're doing enough in training and we're changing the squad around with each game to give us all a chance of being ready."
He was delighted to return to the fray after being forced out of Scotland's World Cup qualifying victory over Croatia due to injury.
The 22-year-old added: "I've just come back, it was the same problem I'd had last season so they thought I could do with a bit more training to improve my fitness before I went into a game.
"I came on at half-time on Saturday and felt good for the 45 minutes I got. I'll do a bit of recovery now and hopefully get a bit of time on Tuesday as well - I want to push on from this now I'm back."
Slotting back into his wide role against Cluj, Forrest looked comfortable in the time he was given on the pitch, and set up Samaras for a late consolation goal.
He said: "It was a hard game, they are a tough team to play against. They have Champions League experience but I thought we did alright. We just need to make sure we are building on each game and moving forward.
"The manager knows we are here to work hard and that was our second game in a couple of days. Obviously he wants better but we're making progress and will hopefully improve for the next one."