The 20-year-old is currently away from the Camp Nou at Sevilla on loan after joining the Catalan giants from Manchester City last year.
Although Suarez is yet to make an outing for Barca’s senior side – he represented their B team last term – Chelsea are already considering a move to bring him back to England.
But a deal for the youngster will have to wait until 2016, with his move to the Ramon Sanchez Pizjuan set to last for two years.
The Blues have been keen on the passer for some time, and initially missed out on his signature when City snapped him up from Celta Vigo in 2011.
The playmaker registered little impact at the Etihad Stadium, making just two League Cup outings before moving back to his homeland in a deal which may rise to £8.1m.
Suarez may eventually end up playing in the same XI as his namesake Luis, who left Liverpool to join Barca earlier this year.