President Trump says Karoline Leavitt is irreplaceable ... though he may have found her successor standing on the other side of a Fox News microphone.

During a Fox News interview, correspondent Alexis McAdams asked Trump whether Leavitt could be replaced. Trump said no, praised her work and joked he was concerned because "she likes her children more than she likes Trump."

When McAdams pressed him on who he wanted behind the White House podium next, Trump turned the question right back on her -- "You? How about you?" -- before saying she could do the job.

Trump even sought approval from Leavitt, who was standing nearby, then told McAdams he had always liked her and praised her work ... noting he doesn’t make offers like that very often.

As TMZ previously reported ... Trump announced Wednesday that Leavitt will leave the role at the end of August to spend more time with her two young children.

She'll remain one of Trump's top outside advisers.

No official replacement has been announced ... but McAdams asked Trump whether he wanted to make news during their interview -- and she may have ended up becoming the news herself!