The 61-year-old was speaking to the media for the first time since he signed a two-year contract to replace Roy Hodgson after the disastrous Euro 2016 campaign which culminated in a 2-1 defeat by Iceland in the second round.
Rooney faces an overhanging threat on two fronts as the arrival of José Mourinho at United - and subsequent deals to sign Zlatan Ibrahimović and Henrikh Mkhitaryan - pose uncomfortable questions over his future role at Old Trafford.
It had been suggested that Rooney’s captaincy of England was a foregone conclusion but Allardyce, speaking at St George’s Park on Monday morning, has moved to deny those reports, citing the infancy of his tenure as the reason for the delay on a decision.
“I’m going to leave that until I meet all the players and get all the staff together,” said Allardyce, before revealing former Bolton Wanderers, Liverpool and Southampton coach Sammy Lee has joined his backroom team.
Allardyce added: “I think that choosing styles or systems depends on the players available and then who we’re playing. My coaching technique is to try and give the players the opportunity to win a football match wherever they are playing, be it home or away. And to make them aware of the opposition, which may change the style of how we play.”
Rooney again struggled to make an impact at a major tournament this summer in France and, at 30, will likely make his final World Cup appearance in two years if England secure qualification to the contest in Russia. His first chance to impress will come when Allardyce's men play Croatia in a friendly on 1 September.
Meanwhile, Allardyce also stressed the importance of striking up positive relationships with Premier League clubs to avoid the club-verses-country disputes which have disrupted the tenures of his predecessors with the national team.
The former Sunderland manager added: “I will try my best to deliver the player back to the football club in the best possible condition. This facility here can allow us to do that. Obviously we cannot predict who will be injured with us but we hope to send them back to their clubs.
“For me, to get around to the Premier League football clubs as much as I can to build relationships will be very important to us as time goes on.”
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