Morgan, a former CNN presenter, has long criticised the couple, saying they have damaged the royal family and sought publicity on their own terms, without the scrutiny that comes with the job.
ITV broadcast Oprah Winfrey's interview with Meghan and Harry on Monday evening.
ITV Chief Executive Carolyn McCall told reporters that she had not spoken to Morgan herself, but Kevin Lygo, managing director media and entertainment, had.
"I know Kevin Lygo is speaking to him on a regular basis and has done so in the last couple of days," she said.
Morgan has cast doubt on Meghan's comments in the interview.
However, when his co-presenter noted that Meghan had said she'd been driven to the verge of taking her own life, Morgan replied: "She says that, yes."
McCall, who was presenting ITV's full-year results, said Morgan had "qualified" his earlier comments on not believing Meghan on the Good Morning Britain breakfast show he presents on Tuesday.
She also said Morgan was a freelance presenter and ITV had no control over his Twitter account.
"He's got personal profile on Twitter, it's his personal account," she said. "If it was about our shows, that would be different."
She said she personally believed Meghan, and ITV was committed to supporting mental health .
"ITV has many voices and we try and represent many voices on ITV every day," she said.
"It's not about one opinion."
ITV reportedly paid 1 million pounds to broadcast the interview, which was shown in the United States on Sunday.
McCall said ITV always followed the big news events and said there had been strong demand for ad slots, adding that the broadcaster would re-use the content in other programmes to maximise the value of the rights.
To be able to write a comment, you have to be registered and logged in
Currently there are no comments.