Former Chelsea and Barcelona forward Gudjohnsen, 36, enjoyed a stint with Wanderers between 1998 and 2000 before moving to Stamford Bridge and he has been back with Lennon's squad for almost a month now.
He played 90 minutes for the club's Under-21s on Monday and Lennon, short of experienced forwards since letting Jermaine Beckford join Preston on loan, revealed the former Iceland international is set to pen terms on a deal until the end of the season.
"I'm assuming everything's agreed," the Northern Irishman said.
"If there's any hold-ups it'll be a minor thing and I'm hoping to have him in the squad for the weekend."
Gudjohnsen could soon be joined by another 36-year-old after Lennon's former Leicester team-mate Heskey was invited to train with the Trotters this week.
The 62-cap England forward is a free agent having left Australia's Newcastle Jets and Lennon has granted Heskey a two-week trial period before deciding whether they will pursue a contract.
"Emile is a free agent, I know him very well from my time at Leicester and he's another player we tried to sign in our time at Celtic," Lennon added.
"He may be coming to the end of his career but he still has very good attributes
It's no-gamble stuff for us, we're just bringing him in and going to have a look over the next 10 days, two weeks - see if he's got something to offer.
"If he has we'll look at it, if he hasn't we'll say, 'thanks for coming in but we're not going to pursue this'."
Lennon is optimistic that Heskey can follow Gudjohnsen's lead and impress sufficiently in his training audition.
It is two years since the Leicester-born forward played in this country but Lennon is confident that despite his advancing years, his talent will not have waned greatly.
"We're pleased he's come in," the Wanderers boss added.
"There's a hunger there to keep playing
He's 36 and he's had a great career.
"We think there might still be a bit of mileage in him yet and if there is we will try and make the most of that.
"If you look at his career, he's won a lot of things in the game and he's played for his country over 60 times now; that's quality and you don't lose the quality.
"You lose the legs a little bit but he was always a fantastic athlete as well
At 36 I still think there might be plenty left in there if he has the right attitude and hunger to keep going.
"I'm really pleased to see the career he went on to have at Liverpool, Villa, Birmingham and obviously England
He's a great kid, always has been
The way he's looked after himself, he's got longevity as well."
Source : PA
Source: PA