Louis van Gaal wants to bring the right-back to Old Trafford this summer, but Monaco are not willing to sell for such a low fee.
It is believed that Leonardo Jardim's side want at least £20m for the Brazil international.
Liverpool have targeted two players as potential replacements for Raheem Sterling, according to the Telegraph.
The Englishman looks certain to leave this summer, with Manchester City and Chelsea both keen.
And it is said that Brendan Rodgers wants one of Monaco's Lucas Ocampos or Dnipro's Yevhen Konoplyanka to take Sterling's place in his squad next season.
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Louis van Gaal is reportedly chasing Monaco's Fabinho
The Ghana international is being lined up for a £15m move to Stamford Bridge after impressing at Augsburg.
It is added that Rahman will arrive as a replacement for Filipe Luis, who looks likely to return to Atletico Madrid after failing to displace Cesar Azpilicueta from Jose Mourinho's starting XI.
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