The Serie A giant is keen to strengthen its team ahead of next season and is looking at the Catania duo for reinforcements.
The Nerazzurri is keen to add some fresh blood to their squad this summer after a disappointing 2012-13 campaign and see the Argentine duo as valuable additions to their roster.
"I would like to make it clear that we have an excellent relationship with Catania and that it quite important," Branca told La Gazzetta dello Sport.
"There's no denying that Barrientos and Gomez are excellent players and their potential has not gone unnoticed. We are in talks with the men in charge at Catania and there will soon be clarity."
Barrientos, 28, has a contract with Catania until the summer of 2015, while the 25-year-old Gomez's has a deal for two more seasons as well.