The Serbian was brought back to Chelsea by current United manager Jose Mourinho in 2014 and has become a target for the Portuguese once again this summer.
Having seemingly been close to a move to Old Trafford earlier in the summer transfer window, it appeared as if the move would be off following United's hijacking of Blues target Romelu Lukaku.
However, the signing now seems imminent with Chelsea owner Roman Abramovich sanctioning a potential £50m ($65m) move following the arrival of the former Benfica player's replacement in Tiemoue Bakoyoko.
Pallister believes it would still be a surprise if Chelsea let him go but claims Matic is a player the Red Devils desperately need.
"Matic is a physical presence and apart from [Marouane] Fellaini we have quite a small midfield," Pallister said, as quoted on the London Evening Standard. "When we looked at United last season we lacked that presence and Matic will certainly bring that."
"He's an excellent player though and it would be a surprise if Chelsea were prepared to let him go."
The former United player has also picked Lukaku as the best forward arrival in the summer window.
With the likes of Alexandre Lacazette joining Arsenal and Alvaro Morata joining Chelsea as the major English clubs looked to bolster their attacking options, Pallister believes the Belgian's experience in the Premier League along with his physical abilities give him the edge.
"I'm going to say Lukaku because he is proven in the Premiership," he added. "The other guys come over to the Premier League and the pace and power is different, but Lukaku has done it regularly for West Brom and Everton."
"He is a proven Premier League goal-scorer, and I think that's why Jose gave up on Morata. Lukaku is very bullish, brash and quick. He'll mess defenders about."