The 66-year-old has set up a group in a bid to improve the development of English football following his comments that there are too many foreign players in the Premier League.
Former Three Lions boss Glenn Hoddle has been named on the commission, as have FA vice-chairman Roger Burden, Football League chairman Greg Clarke, League Managers Association chairman Howard Wilkinson, new Professional Footballers' Association chairman Ritchie Humphreys, Crewe Alexandra director of football Dario Gradi and ex-England defender Danny Mills.
Lineker wrote on Twitter: "No wonder they announced Glenn Hoddle early on @FA commission. Most of the others are utterly pointless. Expected better from Greg Dyke."
Meanwhile, the England senior team are preparing to take on Montenegro in their penultimate World Cup qualifier at Wembley.