The Argentine striker will leave the Etihad when his contract expires at the end of the season, bringing his 10-year stay in Manchester to a close.
Aguero is no stranger to Spanish football, having spent five seasons with Barcelona's LaLiga rivals Atletico Madrid before he joined Man City in 2011.
Sky Sports have reported that the Catalan giants held talks with Aguero's representatives this week ahead of free transfer in the next transfer window.
The 32-year-old has also been linked with Chelsea in the Premier League while there are reportedly a number of other European clubs keen on City's all-time record scorer.
Should he make the move to the Camp Nou, Aguero would reunite with his national side teammate Lionel Messi, although the club are still trying to persuade their captain to sign a new deal.