The champions extended their current unbeaten, winning and clean-sheet sequences with a 4-0 rout of Hibernian at Easter Road yesterday, but the result flattered them and Forster made some significant saves.
Manager Neil Lennon is resigned to Forster wanting to leave eventually, possibly this summer, but he said the club is financially strong enough to reject any bids in the meantime.
"I've never played with a better goalkeeper," said Pukki, who scored one of Celtic's three late goals, with Kris Commons (two) and Virgil van Dijk also on target. "The whole of the dressing room want him to stay for the long term as every player wants to play alongside a 'keeper as good as that."
Lennon said he does expect interest to be expressed in Forster, the England back-up goalkeeper, before the current transfer window closes on Friday night. "It wouldn't surprise me if an offer were to come in. But we're not encouraging it. I'm pretty sure we can knock back a big offer if one comes in. I think he's pretty happy here. I know he's got personal aims in the future but his short-term future, anyway, is with Celtic."
One save from 19-year-old Hibs midfielder Sam Stanton, with the score at 1-0, was "unbelievable", said Lennon. "There are not many goalkeepers who can make those kinds of saves, and thankfully he's one of them. The kid's shot looked a goal all the way. How Fraser got his hand to it and pushed it away, I don't know."
Celtic continued all their precious sequences. They have now gone 22 league games unbeaten since the season started, have won their last 11 league games, have gone 10 domestic games without conceding a goal, and are 15 points clear at the top of the SPFL Premiership. "I'm sure goalkeepers and defenders take a lot of pride in keeping clean sheets," said the manager. "We weren't at our best today, defensively, I must say that. But that's when your goalkeeper has to be called on. You've got to credit Hibs. At that spell in the second half, we were a bit sloppy, a bit ragged with the ball and in our shape. Look, we're not going to get everything our own way all the time. We were worthy winners but the scoreline probably flattered us a wee bit."
Hibs have now lost three games in a row but manager Terry Butcher was philosophical. "We didn't deserve to lose 4-0," he said.
"I told the players they could hold their heads high. It all hinged on the Forster save from Stanton and then the free kick given for a handball [from which Van Dijk doubled Celtic's lead]. In my opinion the handball was bizarre because I don't know anyone who can control a ball hit at that pace with his hand. It wasn't a deliberate handball [by Michael Nelson]. We've been penalised in the harshest way."
Butcher bit his tongue about the referee's performance for fear of provoking a notice of complaint from SFA compliance officer Vincent Lunny. "If I really say what I think about the referee's performance then I would be in trouble with Mr Lunny so I'm not going to go there." When asked if he would raise the matter with the SFA head of referee development, John Fleming, he said no. "That would be a waste of time."