The Russian business tycoon has had difficulties renewing his UK visa in recent weeks.
Having owned Chelsea since 2003, speculation has been rife that the Blues are now on the market.
Reports over the weekend suggested the 51-year-old has turned down an offer from Jim Ratcliffe though.
The mega-rich Brit has an estimated wealth of £20bn – more than twice what Abramovich is worth.
But Gudjohnsen, who knows Abramovich well from his six-year stint as a Chelsea player, doesn’t think he will part with the Premier League giants.
He exclusively told Starsport: “I doubt he’d want to.
“When situations like this arise there’s always going to be questioned.
“I’m pretty sure he’ll be devastated about not being able to go to Stamford Bridge if the situation drags on.
“Abramovich has shown his dedication to Chelsea football club from the moment he arrived.
“I’m convinced he’ll continue to do so in whatever capacity.”
Abramovich’s financial muscle transformed Chelsea into one of Europe’s elite teams.
Gudjohnsen says the reclusive billionaire’s massive cash injection was a game changer.
He added: “It went from a big club to a huge club.
“He changed all the facilities and moved the training ground to Cobham.
“If you look at the facilities now at Chelsea it’s almost a different world.
“We became much bigger after Abramovich because of the spotlight he brought and because of the investment.”
Chelsea has enjoyed unprecedented success over the last 15 years.
They’ve won the Premier League on five occasions and secured a memorable Champions League triumph in 2012.
“Whether he’s still active – and has a connection with the players – I don’t know.
“He just wanted to be near the team and share the excitement of what was happening.”
Chelsea missed out on Champions League qualification this season after an underwhelming campaign.
Gudjonsen, however, reckons the Blues will be back fighting for the title next season.
“I think it’s very clear that Chelsea when they’re playing to their best, can beat anyone.
“It’s a consistency thing. They have the quality and players to be successful. It was just a disappointing season.”