Rear Admiral Kenneth Whitesell, commander of the carrier 2 strike group, was speaking aboard the nuclear-powered super warship USS George HW Bush, which anchored off Stokes Bay yesterday.
His comments came in the wake of a series of tweets sent by American President Donald Trump, in which he proposed a ban on transgender individuals serving in the US military.
When asked by journalists if he was in favour of the president's proposal, Rear Admiral Whitesell said it will be "interesting" to see how the issue and policy "plays out", and stressed he does not have an opinion on it "one way or the other".
He added: "I've got 5,500 sailors that are on board this ship, when you combine the air wing... 7,000 total that operate.
"I'm looking for sailors that can accomplish the mission, and that is all we judge people by."
In a series of posts on Twitter, Mr Trump said he had taken the decision because US forces "cannot be burdened with the tremendous medical costs and disruption that transgender in the military would entail".
Rear Admiral Whitesell, when quizzed about his thoughts and views, added: "Right now our policy is the same thing that was put out by the White House - they are developing policy for what President Trump tweeted about.
"Once he determines exactly how that policy is going to run, then the way our form of military works, the White House will determine the guidelines for it, the Secretary of Defence will then write the guidelines, those guidelines will go to all of the services, then the services will write their guidelines."
Following the proposals made on social media by Mr Trump, UK defence chiefs have since backed transgender people serving in the US armed forces.
His comments have been opposed by Rear Admiral Alex Burton, Commander UK Maritime Forces, who tweeted: "As a Royal Navy LGBT champion and senior warfighter I am so glad we are not going this way."
He added: "We have a justifiably rigorous selection process but it doesn't include discrimination and we're a better fighting force for it."
Second Sea Lord Vice Admiral Jonathan Woodcock said on Twitter he was "proud" of the Royal Navy's transgender personnel.
"They bring diversity to our Royal Navy and I will always support their desire to serve their country," he added.
"I suspect many who doubt the abilities of our diverse service personnel might be more reluctant to serve than they are to comment."
A Ministry of Defence spokesman said it did not comment on "US military recruitment policy".
But the spokesman added: "We are clear that all LGBT+ members of our armed forces play a vital role in keeping our nation safe.
"We will continue to welcome people from a diverse range of backgrounds, including transgender personnel."
The MoD said it was unable to confirm how many transgender people served in the UK military.
Lieutenant General Patrick Sanders, the Army's LGBT champion, said: "The British Army is proud to have many transgender soldiers serving their country and I was proud to march alongside them at Pride this year.
"Like all soldiers, they are prepared to lay down their lives for their country.
"We are a stronger and better Army for being inclusive and we benefit from the rich diversity of all represented in the British Army."
Abigail Austen, Britain's first transgender Army officer, told Channel 4 News she was about to deploy to Afghanistan but had been thrust into an "international firestorm" after President Trump's tweet.
She said thousands of troops now faced an uncertain future.
She added: "When you're sat there in a foxhole, what you really want to know is if the person next to you has got you're back.
"That doesn't matter...whether you're a man, woman or giraffe - it's whether you have the talent to do the job."