The West Ham captain is not thinking about his own chances however.
Allardyce was named as the new Three Lions boss earlier this month after Roy Hodgson resigned following the humiliating exit from Euro 2016.
His appointment has been met with a mixed reception, with some believing he will be perfect and others questioning if his tactics will succeed on the international stage.
West Ham's Mark Noble scores their first goal with a penalty
And he has backed his former manager to be a success with the national side because he’s a great man-manager.
"Do I think England made the right choice? Yes,” he told Sky Sports.
“He knows how to sort stuff out in a way. He's a great man-manager, he knows how to get the best out of his players.”
West Ham's Mark Noble celebrates after the match
The West Ham captain has however insisted he is not thinking about his own international prospects.
There were widespread calls for Noble to be handed his England debut and a place in the squad for Euro 2016 after an impressive season under Slaven Bilic.
Roy Hodgson ignored them though, instead opting to go with other options such as Danny Drinkwater and Fabian Delph before the tournament.
Allardyce was among those calling for Noble to be called up in the past, but the midfielder insists he is just focusing on playing football.
"I'm just concentrating on football - I have since I've started playing," he added.
"Obviously last year I was disappointed, I'm not going to lie to you. I enjoyed a fantastic season with West Ham.”
Sunderland manager Sam Allardyce