According to both Corriere dello Sport and Gazzetta dello Sport (h/t Football Espana), the Bianconeri want to recruit the playmaker as they did with Dani Alves from the Camp Nou.
Iniesta's contract expires this summer, and he is yet to sign a new deal with the club, so he could be set to link up with Alves if he makes the move:
The 33-year-old has struggled slightly for form and fitness this year, and he's in the twilight of his career.
However, the Bianconeri have had great success in recruiting players in his position in recent years, per Bleacher Report UK's Adam Digby:
ESPN's James Tyler also noted their successful transfer policy:
The Serie A giants have been able to rejuvenate and get the best out of those no longer at their peak, and that impressive ability has drawn plenty of plaudits this season with Alves shining since his move from Barca last summer.
If they could do something similar with Iniesta, they would have another asset on their hands.
Football journalist Rafael Hernandez offered a reminder of the Spaniard's almost unrivalled experience at the top level:
However, as Football Espana noted, Iniesta has expressed a desire to end his career at the Camp Nou, where he has spent his entire career.
Juventus would be a tempting option if he does move on, but he may well opt to stay put provided Barca are willing to hand him a new deal, which seems likely.
The right-back appeared unwanted by manager Luis Enrique at the start of the season, and he was given just two outings in the first few months of the campaign.
He fought his way back into the team, though, and made nine appearances between the end of November and early February as he re-established himself as a regular in the side with some excellent performances.
An injury then put an end to his campaign, per Spanish football expert Sergi Dominguez:
Vidal "is ahead of schedule" with his recovery, according to Sport, and he could be fit ahead of next season.
The 27-year-old showed enough to warrant being given another chance at the Camp Nou, but much could depend on the plans of Enrique's successor.