Obama is scheduled to come to Texas for fundraisers on Aug. 9, but White has said he's too busy to meet with him.
But the Democrat said he'd happily take a call from the president.
"I'd be available to talk to the president, whoever the president of the United States is, at any time," White said Friday. "I'm available to talk to anybody by telephone."
Republican Gov. Rick Perry, eager to associate White with Obama in staunchly conservative Texas, says he wants to meet with Obama about border violence while the president is in town.