The French World Cup winner rejoined Juventus in July 2022 following his departure from Manchester United, and has had less than 40 minutes of playing time, coming on as a substitute against Torino and Roma in Serie A.
"He's the first one who is not happy with this year and with this latest injury," Calvo told Sky Sports.
"When it comes to great players everything is emphasised, for better or for worse. I've read big headlines and that Juventus would like to offload him. Absolutely not.
"He arrived here when he was 19, for him it's a family but we are a family that demands a lot. We hope to have him back as soon as possible."
Pogba first joined Juventus in 2012 and won four Serie A titles, two Italian Cups before joining United after the 2015-16 season.
"We believe so much in Pogba, otherwise we wouldn't have signed a four-year contract," Calvo added.
"We are as sorry as he is, we speak daily with the player, he knows we are not happy with this situation just as he is not happy."
