Forrest has been at Celtic his entire career so far and is a very highly rated winger. The 24-year-old has earned 12 caps for Scotland and his contract runs out later this year.
Deila has revealed that Celtic offered the Scotland international winger a new deal, but Forrest rejected it.
The Celtic boss has also suggested that the Scottish Premiership giants will not make a new offer to Forrest.
“We made him a very good offer,” Deila told The Glasgow Evening Times about a new contract for Forrest. “We offered him a contract and he has turned it down. I am disappointed on a personal level because we want to keep all of our good players at the club.
“But it has been made clear that he does not want to sign it. It was a good deal, a very good deal, that the club offered him and I don’t think that there could be any complaints on his part about it. It was a solid offer from the club.
“He has told us that he wishes to see what his other options are. He wants to know what else there is. It is disappointing but I think that will be it from us. I cannot see that we will go back to him with another improved deal because to my mind it was a very good offer that the club put to him.”
Celtic are at the top of the Scottish Premiership table at the moment with 61 points from 26 matches.
The Glasgow giants are six points clear of Aberdeen, who are currently second in the standings.
The Bhoys won 3-0 against Inverness Caledonian Thistle at Celtic Park in the Scottish Premiership at the weekend.
Celtic will return to action on Friday evening when they take on Hamilton Academical away from home at New Douglas Park.