The Argentina defender took aim at the board on social media this week over a disappointing winter market. It was the second time in weeks that Romero has been critical of the club's top brass.
Speaking on Thursday ahead of their clash with Manchester United, Frank insists Romero will retain the captain's armband.
"Leadership is many things," said the Dane. "I am 52-years-old.
"I think I'm pretty good at leadership. Can I get better every single day? Yes. Do I make mistakes? Maybe not every single day but probably weekly.
"Romero is 27-years-old. Is he still going to make mistakes going forward as a leader, does he do a lot of good things? Yes."
Asked about rumours of interest from Atletico Madrid, Frank also said: "That's a question I have no idea about.
"Right now, he is the captain, he has a long-term contract, we signed a new contract with him."