The keeper is back on Teesside waiting to see if the Hammers give the green light for his £4m switch which was agreed last week. Concerns have been raised over his fitness.
Woodgate said, "Randolph is the longest medical in history. It is unbelievable. Let's see what happens over the next 48 hours.
“He is a professional and is an outstanding keeper for us. He will be fine.
“Is he going there to be No2? He is a No1. He is a top keeper. He hasn't gone yet so let's see."