FA chairman Greg Dyke has called on former Three Lions boss Glenn Hoddle, FA vice-chairman Roger Burden, Football League chairman Greg Clarke and League Managers Association chairman Howard Wilkinson to help improve the development of English football.
Following the announcement, former international Lineker described the majority of the members "pointless", which has prompted Mills to call on the Match of the Day host to offer some of his own ideas.
"Gary, come up with your own ideas, volunteer to come on the commission," Mills told Sky Sports News. "Come along to the meetings, give up your time - what are your ideas?"
Meanwhile, England are due to take on Montenegro in tonight's World Cup qualifier at Wembley.