Deila questioned why the Scotland international would move from Parkhead to the Macron Stadium amid reports that Wanderers boss Neil Lennon wants to sign his former protege.
Forrest has struggled with a series of muscle injuries since breaking into Lennon’s Celtic team as a teenager but the 23-year-old was a regular in the last four months of last season.
Deila is keen to keep his squad settled and intact – once again reiterating that Virgil van Dijk will be around for Celtic’s Champions League qualifying campaign – and wants Forrest to build on his improved fitness.
Deila said: “Why go to Bolton? He’s at Celtic.
“I haven’t heard anything. James is a very important player and we want to keep him here.
“He’s now getting to a level where we can start working to get him better. He has been free of injury for six months now, he’s getting more and more consistency in his play and we expect more from him this season than last because of all the injuries.
“It’s a big season not just for him but for everybody. I’m delighted for him because he is such a good boy, it’s good working with him.
“I feel very sorry for him coming in and out for four years now. Hopefully he can continue with his consistency and everyone knows what potential he has.
“But we don’t want to talk about potential, we want to talk about performances. We are going to work to get James up to the level he can reach.”
Deila refused to discuss possible transfer targets such as Genk striker Jelle Vossen, who spent last season on loan at Middlesbrough, and revealed he dropped his interest in new Rangers signing Danny Wilson when Dedryck Boyata joined at the start of the month, replacing his former Manchester City team-mate Jason Denayer.
“We have a lot of options at Celtic,” Deila said. “We went for Boyata at Manchester City and we are very happy with that.
“We only needed one central defender and we got our first choice.
“He’s a great talent and has high ability. He needs matches to get match form, our task is to get his potential out. If we can do that we’ll have a top international player in our squad.
“He’s very hungry to play games and fulfil his own potential and we will help him do that.”
Deila aims to partner Boyata with Van Dijk when Celtic’s Champions League qualifying campaign starts against Icelandic side Stjarnan in mid-July, despite persistent reports linking the Dutchman with a move to the likes of Sunderland, Southampton and Norwich.
Van Dijk fuelled those rumours during a radio interview in his home country just after last season ended but Deila is convinced he will be fully focused over the coming weeks.
“I speak with Virgil all the time – he is very motivated to stay at Celtic,” said Deila, who was promoting Celtic’s upcoming St Mirren Park friendlies against Den Bosch, Dukla Prague and Real Sociedad.
“He enjoys being here every day, he’s a very important player for us and his task is to help us get into the Champions League.
“I’ve been clear to him and everybody else that he is going to stay here for the qualifiers. There’s no contact that I’m aware of.
“He’s one year older, hopefully a year brighter and more experienced. He knows what we do on the pitch is the most important thing.”
Boyata is Deila’s only signing this summer and the Norwegian is relaxed about other attempts.
“We are working on things but the most important thing now is to have a consistency,” he said.
“I’m very comfortable and happy with the players I have. We’ll see if we add to things but first of all it’s the players who have played last season and have done very well.
“Those players can get us into the Champions League and into next season.”