The former Juventus star recently hinted at an exit from Old Trafford.
'Pogba is a Manchester United player, he was with us for many years, he grew up here and we love him, but he is a Manchester United player, ' Paratici said during Sarri's unveiling.
The 19-year-old was excellent for Norwich City last season as he won the EFL Young Player of the Season award after helping the Canaries win the Championship and seal promotion to the Premier League.
He expressed to the media over the weekend that "it could be a good time to have a new challenge".
"For me, I have been for three years in Manchester and have been doing great; some good moments and some bad moments, like everybody".
"After this season and everything that happened, with my season being my best season.it could be a good time to have a new challenge somewhere else". They are even prepared to pay up to £500k a week according to reports by Daily Mail.
How much is Paul Pogba paid by Man Utd?
Romelu Lukaku's future is also up in the air, with the striker being linked with a move to Antonio Conte's Inter Milan, while questions remain over the future of the likes of Alexis Sanchez and David De Gea.
The race to sign Paul Pogba is intensifying with each passing day.
Paratici has spoken of his "fondness" for the World Cup victor.
Real Madrid are believed to have made an opening offer of £90m, but know that it will take considerably more than that to test United's resolve.
Pogba had a prolific season in 2018.
The 21-year-old has also played for Wales, making 11 appearances since his debut in 2017.