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.
Norwich City and Queens Park Rangers are among clubs showing an interest in James Forrest after the Scotland winger rejected a new Celtic contract.