Spanish media outlet Mundo Deportivo, as quoted by the Manchester Evening News, is reporting that the Spanish giants are willing to spend €80m on the World Cup winner this summer.
The same article states that Real Madrid are also prepared to include Bale or Isco as part of a deal for the France international in the current transfer window.
According to the same story, Real Madrid are hoping the chance to sign Isco in particular will prove too tempting for Manchester United to resist.
Pogba has been linked with a potential exit throughout the summer transfer window so far after a difficult third season back at Old Trafford.
Manchester United signed Pogba in a club record £89m deal from Serie A giants Juventus in the 2016 summer transfer window.
Pogba won the Europa League and the League Cup in his first season at Old Trafford to make a promising start to his Red Devils career.
However, the Manchester United star has struggled in the past season or so.
The Red Devils finished in sixth place in the Premier League table last term.
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