Twitter confirmed the meeting to FOX Business on Friday but did not comment further.
A report from The Washington Post said Thursday that the session comes following a week of internal outcry.
"We say that Twitter is what’s happening and what people are talking about right now. Often, we [at] Twitter are what’s happening and what people are talking about. That has certainly been the case this week," Agrawal wrote Thursday in a companywide email, according to the Post. "Following our board announcement, many of you have had different types of questions about Elon Musk, and I want to welcome you to ask those questions to him."
Agrawal said that diversity of views and voices should be "reflected and embraced internally."
Twitter announced earlier this week that it would appoint Musk to its board.
"I’m excited to share that we’re appointing @elonmusk to our board! Through conversations with Elon in recent weeks, it became clear to us that he would bring great value to our Board," Agrawal tweeted Tuesday.
"Looking forward to working with Parag & Twitter board to make significant improvements to Twitter in coming months!" Musk replied.
Hours before, Musk had polled his more than 80 million Twitter followers on whether they'd like to see an edit button on the platform – a popular request.
The company later confirmed that such a button was in process of being developed.
Reaction to the moves was swift, and the Post said several employees had voiced their concerns on the company's Slack channels.
A former Tesla employee reportedly said he was "extremely unnerved" because he saw what the billionaire could do "firsthand."
Some also called Musk's tweets into question and others asked how employees would "reconcile this decision with [their] values."
Twitter executives said the company's liberal San Francisco culture would remain the same and that Musk would not be put in charge of major decisions, calling Agrawal the "tiebreaker."
Nevertheless, Twitter founder Jack Dorsey tweeted that Agrawal and Musk would be an "incredible team."
FOX Business' Jon Michael Raasch, Matt Leach, Danielle Wallace and The Associated Press contributed to this report.