The 23-year-old is currently out-of-action through illness and has been heavily rumoured with a move to Old Trafford, with executive vice-chairman Ed Woodward having reportedly flown out to Barcelona last Monday to discuss a potential deal.
It was widely believed that Woodward had flown out to Spain to discuss a move for Pedro who, of course, has now completed a move to Chelsea, fuelling speculation that a transfer for Neymar isn't perhaps so ridiculous as first seemed.
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However, it is understood that any deal involving the Brazilian could turn out to be more of a long-term strategy than a short one, with the transfer more likely to happen next summer.
The Brazil captain has three years left on his current contract at Barcelona and is a key member of a side that achieved the Champions League, La Liga and Copa del Rey treble last season. Despite this, and especially given the void left by Pedro, United remain confident that they can prise the forward away from the Catalan giants.
It remains to be seen whether Neymar would genuinely be interested in swapping the abundance of trophies available at Barcelona for a United side that scraped their way into the Champions League last season, though it is also believed that the size and history of the Red Devils compels Neymar, who would also like to test his mettle in what is widely regarded as the world's toughest league.