Sunderland boss Allardyce is set to replace Roy Hodgson, who stepped down as England manager following their embarrassing European Championship exit to Iceland in the last 16 last month.
"Clearly the three-man group are convinced he (Allardyce) is the right man," Dyke told Sky Sports. "I'd go along with that as well.
"You'd have to ask them but as far as I understand it that's the discussion. We appointed a three-man committee to go out and look at the candidates and they've come back with a decision about who they think is the best man."
The three-man selection group is made up of FA chief executive Martin Glenn, FA technical director Dan Ashworth and FA vice-chairman David Gill.
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(Reporting by Toby Davis; editing by Amlan Chakraborty)
