The Red Devils have a centre forward at the top of their shopping list going into the summer following the departure of Cristiano Ronaldo and the loan arrival of Wout Weghorst due to end in May.
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Kane is facing an uncertain future at Tottenham with the record goalscorer having just one year left on his contract in north London.
As for Osimhen, the Napoli forward has become one of Europe's most in-demand stars having scored 23 goals in 28 games for the Serie A side.
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With both players in line for potential summer moves, United will have to choose where to focus their attention.
Not many people know more about what it takes to shine in the Premier League as a striker than Thierry Henry and according to the Arsenal legend, it's the Spurs striker who should be at the top of United's list.
Henry told CBS Sport: "Because of the Premier League and he knows the league, if I'm Man United I go Kane.
"That doesn't mean Osimhen is not a good player or whatever, it has nothing to do with that. I think Osimhen can adapt in any league.
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"But if I'm Man United, I would look at it like OK, this guy doesn't need to adapt to anything, he has a way of dropping and can allow Marcus Rashford to run in behind him when he drops. Kane can play anywhere also by the way.
"[Osimhen's future?] We go back to a Chelsea, we go back to a United if I'm thinking Premier League. Paris Saint-Germain would look for a nine because they are looking for a nine. So many teams I'm thinking, where is a nine missing?
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"We know Erling Haaland is there [at Manchester City], let's not talk about Kane and where he's going to go or maybe stay. But those are the teams that I'm thinking are playing without a nine at the minute, or maybe they might lose one, because PSG sometimes use Kylian Mbappe inside, and we all know he's not a nine.
"Is he going to stay or not? But he [Osimhen] is going to go wherever he wants to go. I think he can adapt to a lot of sides."