The London Evening Standard says Woodward is determined to keep hold of the club's record signing – even after Pogba publicly stated his intention to leave.
The £89m midfielder used a promotional tour of Japan to begin the process of trying to secure his Old Trafford.
With two years left on his contract and the option of an additional 12 months, Woodward is in complete control of Pogba's future and under no pressure to sell.
But the France international's comments in Tokyo on Sunday will be of serious concern to United's manager.
He said: “For me I have been for three years in Manchester and have been doing great - some good moments and some bad moments, like everybody. Like everywhere else.
“After this season and everything that happened this season, with my season being my best season as well... I think for me it could be a good time to have a new challenge somewhere else.
“I am thinking of this: to have a new challenge somewhere else."
It's understood Pogba is expected to report for pre-season training at the start of July.