The pair have been training with the club this week, as manager Neil Lennon runs the rule over the duo with a view to a potential signing.
Gudjohnsen previously spent two years at Bolton between 1998 and 2000, before moving on to Chelsea and then Barcelona, where he won several major trophies.
The 36-year-old spent last season at Belgian Pro League outfit Club Brugge and Lennon revealed on Thursday that the former Iceland international is on the verge of agreeing a deal.
"Eidur is close to signing," he said. "With Mark Davies out and Chungy [Lee Chung-yong] maybe unavailable in January, he's someone we felt we needed."
After spells with a number of Premier League clubs, Heskey left England for a stint with Newcastle Jets in Australia's A-League.
Lennon, who played with the striker at Leicester City, will take his time before coming to a final decision on the 36-year-old.
"Myself, [assistant] Johan [Mjallby] and [coach] Garry [Parker] are thinking of comebacks!" he said.
"Emile is a player I know very well. We'll have a look at him and make a decision.
"We're pleased Emile has come in. There is a hunger there for him to keep playing. I've known him since he was 17.
"I feel he can have plenty left in his legs. You don't lose quality. We'll look at him then re-evaluate in a couple of weeks."
Bolton are currently 18th in the Championship.
