The Manchester United forward was handed the armband by Roy Hodgson two years ago, but the new head coach is yet to decide on his own skipper
The forward was handed the captain's armband by Roy Hodgson in August, 2014, shortly after being afforded the Manchester United armband by then-manager Louis van Gaal.
Allardyce, who signed a two-year deal to succeed Hodgson as England manager on Friday, is keen to assess all the players at his disposal and field advice from his backroom staff before making a decision.
"It's far too early to make any predications in that area," he told reporters.
"I’m gonna leave that until I meet all the players and get all the coaching staff in behind the scenes and plan."
Allardyce will take charge of England for the first time on September 1 in a friendly game, widely reported to be against Croatia, before beginning qualification for World Cup 2018.
The 61-year-old is thrilled by his new role and to improve England's morale and performances, but hopes to change the current perception of him.
"I think it was disappointing but i don't think its rock bottom," Allardyce said of England's Euro 2016 campaign.
"I think that part of my expertise is people see me as being able to go into a club and turn it around. I think I'm much more than that to be honest, but that’s a label that I've been given.
"I think I can have a successful journey and a successful journey starts with being together.