The Serie A champions are reported to have begun dialogue with the Red Devils over a deal for Pogba, who departed Turin to re-join United in August 2016 for a then world-record fee after winning four league titles and two Coppas Italia with Juve.
Pogba has often found his form at Old Trafford come under scrutiny and has been touted as a transfer target for Real Madrid, who are undergoing a close-season of rebuilding under Zinedine Zidane.
But the World Cup winner is said to be open to returning to Juve, with the Italian giants rumoured to be considering offering Paulo Dybala, Douglas Costa or Alex Sandro as a makeweight.
Paratici was asked about a move for Pogba and Fiorentina's Federico Chiesa – who is also reportedly on Juve's radar – and he says any transfers are dependent on who replaces Massimiliano Allegri at the Allianz Stadium.
"Federico Chiesa? We certainly have a competitive team, as far as the market is concerned, we await the name of the coach," he told reporters.
"We will make the necessary assessments after announcing it.
"Pogba? The same, we'll speak with the new coach."
Chelsea boss Maurizio Sarri is the overwhelming favourite to be appointed Juve's new head coach and has supposedly told the Blues he wants to leave to take the job.
Paratici said several names are being considered and the club are working hard to assess their options.
"We have very clear ideas about the new coach. We are working, it takes time," he added.
"As I said, we have a range of names, not just one name. There is no time limit, we are working and we are working very calmly."