The Partido de las Doce programme on the Cadena COPE radio station claimed representatives of the capital club approached the Argentinian in 2011, 2013 and 2015, but were rebuffed on each occasion.
Messi, who earlier this month won a fifth Ballon d’Or award for the best player on the planet, has been instrumental in Barcelona’s success in recent years, with the club claiming a Champions League, Primera Division and Copa del Rey treble last season
The report claimed the first approach in 2011 came at a time when Cristiano Ronaldo was being linked with a move to Manchester City. In June 2013 it was reported that a Real executive – on instruction from club president Florentino Perez – made a renewed attempt to sign him after they had lost out to Barcelona in the pursuit of Neymar and with Ronaldo still to commit to a new deal.
The final attempt was made last year, according to the report, after Barcelona had dominated Real in Europe and at home, but again they were knocked back.
Moves between the bitter rivals who dominate the Spanish game are rare, but not unprecedented.
Current Barcelona coach Luis Enrique joined the club from Real in 1996, while, four years, later Perez recruited Portuguese star Luis Figo from Barcelona. Figo’s departure caused uproar in Catalonia and he was targeted by all manner of missiles – including a pig’s head – when he returned to the Nou Camp with Real in November 2002.