Pogba has been linked with a move away from United, where he returned from Juve in 2016.
The 27-year-old sparked fresh speculation over his future when he discussed his happiness to be on international duty, saying "the French national team is a breath of fresh air".
Pogba is reportedly a target for Juventus and LaLiga giants Real Madrid, and former team-mate Marchisio would love to see him back in Turin.
Replying to a tweet from Pogba, Marchisio wrote: "Please @paulpogba.
"Come to @juventusfc… you will be happy again. Me too #tilltheend"
Pogba spent four seasons at Juventus between 2012 and 2016, winning Serie A in each of those campaigns to go with two Coppa Italia trophies and a pair of Supercoppa Italiana crowns.
The 2018 World Cup winner has won the EFL Cup and Europa League since returning to United.
Pogba has made seven Premier League appearances for United this season, with Ole Gunnar Solskjaer's men 14th in the table.
He is without a goal or an assist in the league this season, while his passing accuracy (79.9) is his lowest since arriving at United.
Pogba's 46.1 successful passes and 57.7 passes per 90 minutes are also the lowest since his return to the club, while his 10.9 passes into the final third per 90 is his second lowest.
United return to action when they host West Brom on Saturday.