The Real Madrid star has been heavily linked with a move to Old Trafford in recent months.
Jose Mourinho is a big admirer of the Wales international, 28.
The United boss recently claimed signing Bale was 'mission impossible' for the Red Devils.
However, the Manchester Evening News say otherwise.
They reckon Mourinho has become increasingly encouraged Real will open talks to sell their star man.
The MEN add that the deal is in its early stages but United executive vice chairman Ed Woodward dreams of landing Bale.
Mourinho is desperate to sign a world-class winger and the former Tottenham star fits the bill.
However, Bale is said to be happy at Real.
The winger has won three Champions League trophies since his move to Spain in 2013.
Bale is also the club's second-highest earner behind Cristiano Ronaldo.
