Pukki grabbed a brace in the second leg of their Champions League qualifier against KR Reykjavik last night, adding to an earlier double by defender Virgil van Dijk in a 5-0 aggregate win to secure the Hoops' place in the next round where they will play either St Patrick's or Legia Warsaw.
Forster has been the subject of transfer speculation this summer, but after keeping a clean sheet on Tuesday, his team-mate Pukki made it clear that he wants the England international to stay at Parkhead.
Teemu Pukki scored twice for Celtic
"It's important that we keep Fraser because he's one of the best keepers in the world, so we want him to stay," declared Pukki.
"He's one of the most vital parts of this team, he showed that last season and for a few years before. He's important to the club.
"It might be difficult to hold on to him because there are many teams after him. But personally, I hope he stays because he's a great 'keeper."
Celtic manager Ronny Deila echoed Pukki’s thoughts in his post-match press conference.
"We want to keep Fraser. Of course we want to qualify for the Champions League so we want to keep him," said the Norwegian.
"He hasn't [indicated a desire to leave]. He has done a good job since he has come to Celtic but Celtic have also been fantastic for him and I hope that will continue because we need our best players and he is a fantastic 'keeper.
"Something will happen in the end but if it happens now or in the winter or next summer, I don't know, we will see. But we have to keep on going.
"Things are happening around my players all the time but Fraser is an unbelievable professional and I know that he really wants to play in the Champions League."
