The Arsenal legend has previously endured unsuccessful spells as manager of Monaco and Montreal Impact.
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Either side of his forays into management he assisted Roberto Martinez with Belgium.
With the Spaniard having now moved to Portugal, Henry has different plans – amid links with the US national team job.
Asked about the rumours while appearing as a pundit on CBS Sport’s Champions League coverage this week, Henry said: “Would I put my name in the hat?
“First and foremost it is a tricky one to talk about here [on TV].
“Roberto Martinez went to coach Portugal and I’m not going to follow him.
“Being a number two is not something I would like to do anymore.”
On getting back into management, he added: “I would love to have a crack at it again.”
And on the US job specifically, the 47-year-old continued: “What is the plan? What is the philosophy?
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“Just because you will be a host nation doesn’t automatically mean you will go far in the competition.”
The US are set to co-host the 2026 World Cup alongside neighbours Canada and Mexico.
Henry finished his playing career with New York Red Bulls between 2010 and 2014.
He then managed Canadian side Montreal in MLS between 2019 and 2021.
The former striker has underwhelmed so far as a manager.
He won just four of his 20 matches in charge of Monaco, lasting only 103 days in the job.
Henry then won nine of 29 games at the helm of Montreal.
His fellow pundit Jamie Carragher cheekily said: “Come on US Soccer, you know what to do, appoint the man!
“All you have to do is stop the MLS for a couple of months, and he’s in.”
Micah Richards then chimed in: “No no no, don’t leave me Titi!”
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