Sheringham was unveiled as the League Two club’s new boss on Thursday having spent a season under Allardyce as West Ham’s attacking coach.
Allardyce is out of contract this summer and widely expected to leave the Hammers after their final game of the season away to his former club Newcastle on Sunday, but Sheringham says his old boss has not yet abandoned hope of landing a new deal.
And the former England striker has admitted he would have been happy to stay at Upton Park had he known Allardyce’s future was secure.
But when Stevenage called “out of the blue” to offer him the job to replace their outgoing coach Graham Westley, Sheringham knew it was the right time to make his full managerial bow.
He told Sky Sports: “If Sam had asked me three or four months ago and said, ‘Look, I’ve got a couple more years here and I want to you stay’, I’d probably have said, ‘Yeah, let’s do it’.
“But things have been uncertain for Sam in the last six months and things have dragged on from his perspective, which has left an empty corridor for myself.
“I thought to myself over the last couple of months I could give it a go, but for this chance to come up out of the blue it feels right so I am going to jump in and take a chance.
“(Allardyce) is still hopeful that something will happen – it happened like that the last time he was out of contract at West Ham.
“I don’t think it’s any mystery or secret that they have been trying to look for other managers. (But) just because… the next contract isn’t straight at his feet doesn’t mean to say that it’s not going to happen.”