The Frenchman sparked wild speculation last week while on international duty when he said playing for "Real Madrid is a dream for anyone".
And former United winger Thornley, who works a commentator for MUTV, thinks the club cannot afford to lose the 26-year-old.
Asked if he believes the World Cup winner will remain at Old Trafford, Thornley told TribalFootball.com: "Yeah I hope so. Players like Paul Pogba are people that who need to build your club around.
"He's got longevity on his side, he's got great skill, as long as he uses that skill in the correct areas and if his attitude and mindset is spot on, there are very few better midfielder players and more influential midfield players in the world."The new comments about Real are an unwelcome distraction, according to Thornley, who believes it would be a poor decision for Pogba to swap United for a Madrid side, who have been knocked out of the Champions League and are set to finish behind Barcelona in La Liga for a fifth time in six seasons.Thornley added: "I, for one, hope he (Pogba) stays and can visualise what direction Manchester United are going in and knowing that he is an integral part of making sure that that's where they are going.
"I just think that for him to be mentioning other clubs, he just needs to forget all that. We had it with Juventus when Mourinho was there, and yes I appreciate that Zidane has taken over at Madrid, but I think Madrid are a team in transition now and they are going to have to start building from the bottom again. I think Manchester United are further ahead than Real Madrid and I think Paul Pogba needs to stay and be a part of that."