The Chelsea defender retired from England duty in 2012 having twice been stripped of the captaincy and was never considered an option by previous manager Roy Hodgson.
But, with 78 caps to his name, Terry – now considered a veteran at 35 – could make an unexpected return if Allardyce opts to offer him an opportunity to do so.
Allardyce said he would want to be fully aware of any lingering politics surrounding Terry’s past, which saw him lose the captaincy first in 2010 following stories over his private life and again in 2012 after allegations he racially abused QPR’s Anton Ferdinand, but the former West Ham and Sunderland boss revealed a conversation may take place in the future.
Asked if Terry was back in the England equation, the Three Lions manager replied: “I don’t know what the political side of that might mean, if there is a political side. I’ll have to have that conversation if I feel that John Terry may be a possibility.
“I think it depends on what John said. Maybe if I get the opportunity, I might have to give him a ring. But until I come to that selection or that process, we’ll wait and see.”
Allardyce, 61, will name his first squad on Sunday ahead of a World Cup qualification opener in Slovakia a week later.
He has yet to name his captain but has confirmed Joe Hart will remain part of his squad for the moment despite the goalkeeper falling behind Willy Caballero in the pecking order at Manchester City under Pep Guardiola.
Another City player fully expected to be involved in recent signing John Stones, with the centre-back having started all three games since joining from Everton earlier in the month.
While Allardyce wants instant results rather than the promise of potential from his squad, he said the 22-year-old has already shown he is good enough for the job.
“See there’s that word then, we don’t want potential do we. I want the thing, and right now,” he said when asked about Stones.
“Potential is something that’s going to be great in the future. I want it right now and I think he’s got a great chance of becoming right now working with Manchester City.
“With all due respect to Everton, working with Manchester City and the level he has to get to because you don’t realise he (Guardiola) does focus quite a lot on defending – not just wining the ball back.
“(Gerard) Pique was a little similar at Man United until he went to Barcelona then he became a good defender as well as a great attribute for Barcelona in possession. So he had both. That’s why he stayed there for so long.”