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The 49-year-old former striker enjoyed a prolific playing career with the Red Devils and forged a memorable partnership with Dwight Yorke.
Speaking to The Daily Mail, Cole said that Arsenal icon Henry and Premier League legend Shearer were both "a given" in his picks.
And the former Blackburn Rovers and Newcastle man revealed his other three choices would include Manchester City star Sergio Aguero, United legend Wayne Rooney and ex-Red Devils striker Ruud van Nistelrooy.
"[Sergio] Aguero, he would definitely be in there," Cole said.
"Rooney would be in there, [Ruud] Van Nistelrooy would have a shout [...]."
Cole spent six years at Old Trafford and won five Premier League titles, two FA Cups and a Champions League.
The former United star refused to name himself in his top five picks, saying "everyone would be telling me how arrogant I am" for doing such a thing.
Cole explained: "You can say that. The perception everyone has of me is arrogant [...] if I was to put myself in the top five, everyone would be telling me how arrogant I am.
"Everyone wants to talk about what I've done in my career, the goals I've scored, but no-one wants to give me the credit for doing it. I would never put myself in that top five."
Shearer, who is widely regarded as one of the best strikers of all time, remains the Premier League's all-time record scorer with 260 goals.
Rooney remains in second place with 208, while Cole is third with 187 goals and Aguero is fourth with 180 goals.
Featured Image Credit: PA
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