Van Persie is a top target for United boss Sir Alex Ferguson.
"He's a player a lot of clubs would be interested in," Pallister told talkSPORT. "He was unbelievable season last year and over the years he's proven that, when he's fit, he's got all the qualities you need to lead the line in Premier League football.
"Van Persie's signing could be the boost that sees Man United win the Premier League title this season.
"The disappointment of last season will have cut them very deeply. Going into any new season you like to have the influx of new blood because it lifts the dressing room and the fans.
"Signing Van Persie would be a huge lift because he's unstoppable when he's on top form. He'll get them loads of goals."