The 24-year-old, whose current contract ends at the end of 2016, was offered a four-year extension by the Scottish Premiership leaders in January.
Forrest came through the youth ranks with the reigning champions, for whom he has made 144 appearances.
However, his outings have been restricted by a series of injuries.
Forrest, who has 13 Scotland caps, was missing from Celtic's squad for Saturday's 3-0 victory over Inverness Caledonian Thistle.
Celtic signed Manchester City winger Patrick Roberts on an 18-month loan deal from Manchester City in January and last week secured a summer move for 17-year-old midfielder Kristoffer Ajer from Norwegian club Start.
Deila admitted on Saturday that Celtic had too many midfielders on their books and that he would have to slim his squad at the end of this season.

There are concerns the report will not be released before the 2015 election.
Some MPs have blamed hold-ups on a reluctance to release correspondence between Mr Blair and President Bush.
But the ex-Labour prime minister said he was not blocking any documents and publication would allow him "restate" the case for the 2003 invasion.
The inquiry, which is examining the UK's participation in the military action against Saddam Hussein and its aftermath, began in 2009 and its last public hearings took place in 2011.
Although the inquiry team, led by Sir John Chilcot, has never set a target date or deadline for publication, it is generally accepted that the timetable for publication has slipped on several occasions.
David Cameron has said he hopes the report will be released before the end of the year.
Mr Blair, who appeared in person twice before the inquiry to justify his decision to take the UK to war, said he had an interest in the report being published as quickly as possible.
"It is certainly not me who is holding it up," he told BBC Radio 4's Today programme. "The sooner it is published the better, from my perspective, as it allows me to make the arguments."
In its last update, in November, the inquiry said making progress was dependent on the "satisfactory completion" of discussions about the disclosure of private material, including 25 notes from Mr Blair to President Bush and more than 130 records of conversations between either Mr Blair or Gordon Brown and the former US president.
Asked about this, Mr Blair said the inquiry has had the documents in its possession "for a long period of time".
"Obviously there are whole load of issues to do with confidentiality that have to be resolved - as far as I am concerned the government is resolving them."
The former Labour leader was asked whether he believed the US government was responsible for the apparent hold-up.
"I do not know what the reason for the delay is because I am not in charge of the inquiry and I am not in charge of the government. All I can tell you is it is not from me and I resent the suggestions that it is.
"I have as much interest as anyone seeing the inquiry publish its findings and to be able to go out and, frankly, restate my case and defend my position."
The final decision about the publication of UK documents will be taken by Cabinet Secretary Sir Jeremy Heyward. MPs have said they may call him to a Commons committee hearing to explain the state of affairs.

The chorus of Taylor's new single Look What You Made Me Do follows the same rhythmic pattern as I'm Too Sexy.
After the song was released overnight, the duo tweeted: "Thank you Taylor Swift, what a marvellous reinvention!"
The group's spokesman confirmed to the BBC they were approached by Taylor's team in advance of the release.
Norwich City and Queens Park Rangers are among clubs showing an interest in James Forrest after the Scotland winger rejected a new Celtic contract.
[NEXT_CONCEPT]
Tony Blair has said he wants the Iraq Inquiry report to be published as soon as possible and "resents" claims he is to blame for its slow progress.
[NEXT_CONCEPT]
Right Said Fred have been credited as writers on Taylor Swift's new single in one of the most bizarre musical combinations of the year.