The former Tottenham and Manchester United striker was unveiled as the new manager of League Two club Stevenage on Thursday and he says the doubt regarding the West Ham manager helped him move on from his coaching role at the east London club to take the reins at Boro.
"If Sam had asked me four months ago, I probably would have stayed another year. But the uncertainty (with Allardyce's position) left things open," said Sheringham.
"This chance then came about, they took a gamble on me, and it felt right.
"When I had the approach, I spoke to family but professionally it was just Sam.
"As soon as I said Stevenage, Sam said, 'Take it, I've heard the chairman is very good'."