The Talksport host, who is widely assumed to be a Gers supporter, claims to have spoken to Defoe on Friday morning.
It was reported on Thursday that Rangers are set to sign the 36-year-old on an 18-month loan from Bournemouth.
But it is first stop; Manchester, according to White.
"I’ve spoken to him this morning - he’s still down here," the Glaswegian told Friday's Alan Brazil Sports Breakfast show. "He is absolutely raring to go. He can’t wait to get started.
"He’s waiting on a call to go to Manchester for the medical this morning, personal terms have been agreed, the whole thing.
"I think it’s going to be sensational. He’s broken records everywhere."
Defoe is expected to be joined at Rangers by the Southampton midfielder and captain, Steven Davis.
The pair look set to replace Umar Sadiq and Ovie Ejaria, respectively, at Ibrox.
It is also reported that Jordan Jones, the Kilmarnock winger, and Glen Kamara, the Dundee midfielder, could sign pre-contract deals with Steven Gerrard's side.
Rangers are level points with Celtic at the top of the Scottish Premiership, although the seven-in-a-row champions have a game in hand on their Old Firm rivals.
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