A former player might not be the right person to be the new chair of the Football Association because they lack financial and business experience, says the FA chief executive Mark Bullingham.
Ex-Chelsea defender Paul Elliott and Gary Lineker have been suggested.
But Bullingham said the FA needs candidates “who can run the board of a £450m business”.
Speaking to BBC sports editor Dan Roan, he added: “Some players will be capable of doing that but some might not have the experience.”
Elliott, currently chairman of the FA’s inclusion advisory board, has been backed for the role by former England international Sue Smith.
And other former players, such as ex-England striker Lineker, have also been suggested.
Bullingham said: “We need the influence of former players on our board.
“If you look at the two different components of the role: one we want a fantastic ambassador – there is no question players can do that – but secondly we need someone who can run the board for a £450m turnover business.”
Elliott, 56, who also played for Charlton, Luton, Celtic and Pisa, is on the FA Board but does not have voting power.
Former Reading and Hull defender Liam Rosenior, the Derby first-team coach and another member of the inclusion advisory board, is part of a six-person panel which will oversee the process to recruit Clarke’s successor.
“We really wanted someone who could represent the ex-playing community,” Bullingham said. “He’s also a current coach and felt with him we were covering all areas of our game of our panel.”
Bullingham said it was “critical” there was a diverse shortlist but said the FA would “choose the best candidate from that shortlist” when asked if there would be pressure to have a non-white chair.
“To do it any other way would be wrong and disrespectful to the communities you’re talking about,” he said.
Clarke resigned on 10 November because of the “unacceptable” language he used when referring to black players when speaking to the Department for Digital, Culture, Media and Sport (DCMS) select committee.
He prompted further criticism when referring to gay players making a “life choice” and a coach telling him young female players did not like having the ball hit hard at them.
Bullingham added that staff at the FA had been upset by Clarke’s comments.