The Spanish champions are believed to be in the market for a new attacker due to the fact that Ousmane Dembele is set to miss the remainder of the campaign with a hamstring injury.
La Liga clubs are able to sign players outside of the transfer window if they suffer a long-term injury - five months or more - during the season, and Getafe's Angel has been strongly linked with a move to Camp Nou.
However, according to Deportes Cuatro, Stuani is the preferred target for Quique Setien's side as the Catalan giants search for a new forward.
The 33-year-old, who is believed to have a €20m (£16.9m) release clause in his current deal, scored 19 La Liga goals for Girona during the 2019-20 campaign.
The former Middlesbrough striker has also been in excellent form in Spain's second tier this term, finding the back of the net on 20 occasions in 22 appearances.
As well as Dembele, Luis Suarez also faces a battle to return before the end of the campaign having undergone a knee operation towards the start of January.