The Brazil international is available from Barca after spending last season on-loan with Celta Vigo.
Sport says Barcelona will demand £14.3million for their academy graduate, who joined the club aged 13.
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.
But despite being keen to get a deal over the line, the Galicia side were unable to stump up the cash and Rafinha is keen on testing himself in the Premier League.
Leeds are thought to face some competition for the midfielder, who is the younger brother of Thiago.
Thiago, 29, also came through at La Masia but only spent three seasons as a first-team regular before joining Bayern Munich in 2013