An ex-player will find it tough to fulfill the criteria to become Greg Clarke’s successor as Football Association chairman, the governing body has admitted.

Baroness Sue Campbell, the FA’s director of women’s football, remains a likely candidate after chief executive Mark Bullingham also said over-65s can apply.

Bullingham promised an appointment will be from a diverse pool following Clarke’s career-ending comments to MPs on sexuality, race and women’s football.

Liam Rosenior, Derby’s first-team coach and FA inclusion board member, was named on a recruitment committee in the absence of the sub-group’s chair Paul Elliott, who has yet to rule himself out of applying for the role.

However, the likelihood of most former players getting the role is in serious doubt after Bullingham said "it’s hard to see that someone who has never run a board would be able to step in and run a complex stakeholder board of a £450million organisation". Another early favourite, Stacey Cartwright, a non-executive director formerly on the board at Liverpool, is also out of the running for the job as she instead chairing the panel working through a shortlist in the coming weeks.

Bullingham admitted finding a successor for Clarke was "a critical appointment" after a "really challenging 10 days for the organisation since Greg’s departure".

The age limit rule of 65 for the FA Council would not be an obstacle for the next chairman, Bullingham suggested. Early frontrunner Campbell, the FA’s director of women’s football who chaired UK Sport in the run-up to the London Olympics, is 72. "Let me just say that for us there is nothing about the appointment where we’re prioritising any physical characteristics," he said. "Our priority is to have a really good and diverse shortlist and  choose the best candidate."

Bullingham declined to comment on names but said he was excited about the pool of talent that had already come forward to express interest. Unlike previous appointments, they will not advertise the role in a Sunday broadsheet and they are not planning to use the same three recruitment firms that were used for previous appointments. The issue had first been raised in The Telegraph by anti-discrimination campaigner Piara Powar and Bullingham said "I agree completely with the point."

"This will be a process that will be very different to the last one," he said. "Hopefully you see that for the panel. We are doing our assessment of the agencies. We had over 20 agencies come forward and we’ve already started on a shortlist. In that shortlisting  we want an agency or possibly multiple agencies that will help us find the most diverse candidate. So I think you’ll see we’re looking well beyond the usual suspects."

Given Clarke had previously got into trouble over comments on race to the Digital, Culture, Media and Sport Committee in 2017, the 63-year-old’s comments about "coloured footballers", "Asian IT workers", schoolgirl footballers and the suggestion that being gay is a "life choice" appalled Bullingham.

Asked if any former player could have the necessary corporate experience, Bullingham said: “Possibly, but I think it’s a tough ask. I’m not saying no but I do think it’s difficult. There are two main areas of the role, one to be an absolutely brilliant ambassador and to represent us on the international and domestic stage, and I think players can absolutely do that. There is a separate requirement to run the board; we do have a complex stakeholder board and I think it’s hard to see that someone who has never run a board would be able to step in and run a board of a £450 million organisation. That’s not to rule anyone out, that’s just to give you my views on the different skill sets required.”

Cartwright, who is a former chief executive of Harvey Nichols, will chair the recruitment panel, supported by interim FA chairman Peter McCormick and board members Rupinder Bains, Jack Pearce and Kate Tinsley.