The 24-year-old is set to be rewarded for continuing to impress at Parkhead.
Deila claimed that although the 24-year-old has struggled with injuries at times, he could prove to become a fantastic player for the Bhoys, and thus it is imperative for the club to tie him down for longer.
"James is definitely the next that we would like to get in and sign a new contract and get it out of the way," he said. "James and I speak all the time and we would be hopeful that he will agree new terms to stay because he is another important player for us.
"We have started to see the form he is capable of this season and when he is fit and pain free he is a great talent. We would love to get him signed up. Hopefully that will happen. He is happy here and we are happy with him.
"He wants to stay and we want him here so it should not be a problem. He can be a big player for Celtic because he is very talented. We just need to keep him fit and injury free."
Since making his debut in 2010, Forrest has impressed many with his pace and dribbling ability.
His form has seen him earn international recognition with Scotland, and he will no doubt be an important member of Gordon Strachan's squad as they desperately try to put the disappointment of missing out on Euro 2016 behind them, and look to qualify for the 2018 World Cup.
This season Forrest has featured regularly for Deila's side but his only goal so far came in the top of the table clash with Aberdeen in October. With Celtic already two goals ahead, Forrest's goal effectively killed the game off, and ensured that Adam Rooney's late reply was nothing more than a consolation.