Shaw has continued his excellent domestic form at Euro 2020, delivering two assists for England in their quarter-final win over Ukraine.
And United team-mate Mata never doubted Shaw's ability as he backed him to become a star.
Mata signed his autobiography for Shaw with a strong personal message.
It read: "To my friend Luke, you can be the best left-back in the Premier League, believe it!"
25-year-old Shaw is contracted at Old Trafford until 2023 with the option of another year.
It is understood United are hoping to reward him another bumper deal.
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