The Brazil international is available after spending last season on-loan with Celta Vigo
The La Liga giants will demand around £14m for their academy graduate, who joined the club aged 13.
He has featured 90 times for the senior side, scoring 12 goals, since making his first-team debut in the 2011/12 season but has been loaned out to Celta Vigo and Inter Milan.
Rafinha, 27, spent last season back at Celta who had the option to make the switch permanent for the same fee Barca are quoting to Leeds.