The Colombian star – who is not at the World Cup due to injury – is widely seen as one of the planet’s best strikers, and only joined his current side in a £52m deal last year.
But ever since his arrival on the Mediterranean coast there have been rumours circulating that his stay will be s short one, and now it appears that it may well end in the coming months.
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This has alerted the Premier League trio, who are all ready to offer him an escape route.
Chelsea are understood to be at the front of the queue, with the Blues having been close to snapping him up in the past.
Diego Costa is thought to be on his way to west London, but that may not stop Jose Mourinho from adding Falcao after bringing in £90m from player sales since January.
City are also in the battle amid rumours that Alvaro Negredo is ready to leave the club, while Liverpool may turn to Falcao if Luis Suarez leaves for Real Madrid or Barcelona.