The England international played in Tuesday's 4-0 victory over Icelandic club KR, which secured a 5-0 aggregate win and progression to the third qualifying round of the Champions League, just hours after the Scottish champions had reportedly knocked back an offer from Southampton.
Deila says that Forster has made no attempt to leave Celtic Park but struggles to see him staying where he is beyond another year at most.
"In the end, something will happen with Fraser," he told the press, "but whether it happens now, in the winter or next summer, I don't know.
"I want to keep him because I want to qualify for the Champions League and build this team further.
"We want to keep him here. He has given me no indication he wants to leave. He is an unbelievable professional and I know he wants to play in the Champions League."
Forster has played 140 league matches for Celtic over four seasons with the Glasgow club, winning the last three league titles and the Scottish Cup in 2011 and 2013.
The Newcastle youth product was part of Roy Hodgson's 23-man squad for the World Cup in Brazil but has only played two matches for England.