Welker interned at NBC News more than two decades ago.
The match-up will run over two nights, June 26 and 27.
Brokaw told “Meet the Press” many people fear the “intermarriage that is going on.”
“Megyn Kelly is no longer an employee of NBC,” the network said in a statement.
“The 9 a.m. hour will be hosted by other ‘TODAY’ co-anchors,” a spokesperson said.
Anchor is reportedly being shunned by Hollywood stars, talent agents and NBC colleagues.