"We have enquired about him," Stoke chairman Peter Coates told newspaper The Sentinel.
"We have talked about getting him on a 12-month loan because we think he could be a good player for 12 months, and maybe after that."
Gudjohnsen was brought to Bolton from club football in Iceland by manager Colin Todd in 1998.
Would Gudjohnsen fit in at Stoke?
The striker then moved to Chelsea where he spent six years, winning two league titles and a League Cup under manager Jose Mourinho.
He then moved to Barcelona in 2006 and helped the Catalan side to 2009 Champions League glory.
Source: BBC Sport
Source: BBC Sport