The 26-year-old is ready to make his bow in the crunch game with co-hosts Ukraine on Tuesday after serving a two-match suspension and Pallister is certain that he will make an immediate impact.
“So far been kicking his heels in the stands and knowing the type of kid that he is, Wayne will be really eager to get back into the fray and watching his team in action will have only served to have whetted his appetite,” Pallister told Goal.com.
“The break will have probably helped Wayne. He will be fresh and he will be keen. Now it is just a matter of Roy Hodgson unleashing the beast against Ukraine.
“Wayne is a world class player and when he is at his very best he is certainly right up there with the top players in world football. He is the one player that England fans will get really excited about when he is in the side.
“There is so much expected of him when he is playing but that won’t bother him. I feel as though he owes his teammates and maybe the England fans a big game because of the ban."
Pallister also expressed his belief that Rooney should be partnered in attack by Manchester United colleague Danny Welbeck rather than Liverpool striker Andy Carroll.
“I think that Wayne should link up with Danny Welbeck,” Pallister added. “Andy did okay in the game against Sweden but Danny and Wayne know each other really well and they have linked up well this season and it will suit them both if they play alongside each other.
“I think that Roy Hodgson will go with Welbeck because he is more of a threat than Andy Carroll and he is more of a natural goal-scorer than Andy Carroll so I expect that is the way he will go.
“Defenders don’t particularly like pace and Danny has got that in abundance. He is still learning the game in terms of holding up the ball and being a team player but even though he is not the finished article he is still a cracking player."
England has made a promising start to the tournament - posting a draw with France and a win over Sweden to earn four points - but Pallister has played down his compatriots’ chance of glory.
“Overall England have done okay and they have probably surpassed expectations,” the former Middlesbrough player added.
“Everyone expected them to be beaten by France – myself included if I am being honest – and Sweden made it harder than it possibly should have been but we are sat in a good position in the group going into the Ukraine game.
“At this moment I think we have done very well but I think it is too big a task to go on and win it. But we have certainly done better than a lot of people would have expected already.
“I know that Roy Hodgson has only had a short time to work with the England side so to get the results they have achieved so far means that he deserves a pat on the back.”