Giuseppe Marotta said the Serie A giants had not put a price tag on Dybala, who has also been linked with 12-time European champions Real Madrid.
Reports last week suggested United boss Mourinho had set his sights on Dybala to strengthen his attack and was hoping the Argentine's former Juventus teammate Paul Pogba could help convince him to move to Old Trafford.
After Barcelona announced they had agreed to sign Philippe Coutinho from Liverpool in a £142m deal on 6 January, Marotta was asked what price Juventus would demand for Dybala.
"We haven't put a price tag on Paulo, so it's difficult to make an assessment," he was quoted as saying by Football Italia. "We have no intention of putting him on the market.
"The January transfer window is about repairing your squad and fortunately we are covered in all departments," Marotta added.
Juventus coach Massimiliano Allegri, meanwhile, claimed Dybala could not play as an out-and-out striker for a "big club" and was more suited to playing a deeper role.
"He cannot play centre-forward for a big club, where the distance to goal is much shorter," Allegri was reported as saying by Goal.
"Just look at his best goals for Juve, they're often when he's running from deeper positions."
The former AC Milan boss added the Dybala's form had taken a hit this season due to him being compared with Barcelona forward Lionel Messi and Real Madrid's Cristiano Ronaldo.
"The comparisons which were made at the start [of the season] were damaging for Paulo, but fortunately he's a smart lad and he understands you can't compare a lad of 24 to two sacred monsters of football [Messi and Cristiano Ronaldo], who have won 10 Ballons d'Or," he said.