The Hoops boss wants to hold on to the shot-stopper for seasons to come.
Southampton have had what Celtic describe as a derisory offer for the No.1 rejected, but are expected to come back with a figure much nearer the £7.5million Celtic rate him.
The 26-year-old left the field after claiming another shut-out last night against KR Reykjavik with his top and his gloves in his hand.
But nothing was thrown to the fans by way of a farewell gesture. And Deila wants to keep it that way.
He said: "We want to keep Fraser because we want to qualify for the Champions League and build our team.
"We want to do what we can to keep him here."
Deila confirmed Forster is not agitating to get away and said: "He came to Celtic and did a good job, but Celtic have also been fantastic for him.
"And I hope that will continue because we need our best players.
"He is a fantastic goalkeeper.
"We will see because in the end something will happen.
"Whether that's now or in the winter or next summer I don't know.
"We have to keep on going and things are happening around my players all the time.
"But they have to train good every day, and that's one of Fraser's best skills.
"He is an unbelievable professional and I know he really wants to play in the Champions League."