Cole joined the Scottish Premiership giants in October 2015 and has a contract with the Glasgow-based outfit until June 2017.
The former Chelsea and West Ham United striker was signed in order to add depth to the Celtic squad.
The Englishman, though, has not performed as expected and is not guaranteed playing time even as a substitute.
Cole has been given leave of absence by Celtic for personal reasons, and Deila has suggested that the striker will remain at Celtic Park beyond the summer.
“Carlton has not trained for a while now because he has some things he has to do,” the Norwegian told Herald Scotland.
“Carlton is a fantastic person and a good player. There’s not so long left in the season now. We have to see what’s happening in the future.”
Cole is a decent striker, but he is not the player who can take Celtic to the next level.
The Bhoys need someone who can help them negotiate the tricky Champions League qualifiers, and the former West Ham striker is not going to be able to do that.
Celtic are at the top of the Scottish Premiership table at the moment with 63 points from 28 matches, a point clear of second-placed Aberdeen, who have played a game more.