England women's coach Middleton unconcerned if successor male or female
Middleton will step down after the Women's Six Nations Grand Slam showdown against France at Twickenham on Saturday.
England have reached two World Cup finals and won five Six Nations titles and four Grand Slams during his time in charge.
The Red Roses also recorded a 30-game unbeaten run that ended with the crushing disappointment of a defeat by New Zealand in last year's World Cup final.
Sarina Wiegman's success in leading the England women's football team to a Euro 2022 triumph has led to fresh suggestions that a female coach should succeed Middleton.
"We have got some very good coaches/directors of rugby-style females in the game," Middleton said Wednesday.
"Giselle Mather (Ealing Trailfinders director of rugby) is one, Jo Yapp (Worcester women's head coach) being one, Susie Appleby (Exeter head coach) being another.
"A lot of it is relevant to the team you build around you and how you manage that team of staff. The right person will be the best person."
'New drive'
It was a view backed up by England captain Marlie Packer, set to lead her team out in front of a record crowd for a women's match of more than 53,000 at Twickenham on Saturday.
"For me, I think it is the right person for the job," she said. "Whether it is a male or female, I don't mind. I think that is what most of the squad think as well.
"We just want to be pushed as players to be the best players we can. We want someone who is going to give us a new drive, and it doesn't matter who it is."
England have piled up 233 points and conceded a mere 15 in their opening four matches of this Six Nations.
But they now face their strongest European opponent, with France unbeaten as well heading into the last round.
Middleton, keen to take the focus off himself, added: "The magnitude of the game this weekend is a huge distraction from potentially everything else.
"It has been a real privilege to be part of it, and we just desperately want to make sure we finish it in the right way on Saturday. What we want is more occasions like this one."
Middleton has made four changes to the team that defeated Ireland 48-0 in Cork last weekend - the only time so far this Six Nations that England have failed to score 50 points.
Helena Rowland makes her first start of the campaign, partnering Tatyana Heard in midfield, while scrum-half Lucy Packer, hooker Lark Davies and prop Sarah Bern are also included.
Packer, who went off injured against Ireland, packs down in the back row with Sadia Kabaya and Alex Matthews.
"It is going to be a very special occasion," Packer added. "To lead the squad out for a Six Nations Grand Slam decider is going to be epic.
"Simon will leave a massive legacy. The group has massive respect for him, what he has done for us as a group and for the women's game.
"When he told me he was leaving, I gave him a hug and said, 'Right, let's go and win this Six Nations, let's send you off properly'."
England team to play France (15-1)
Ellie Kildunne; Abby Dow, Helena Rowland, Tatyana Heard, Claudia MacDonald; Holly Aitchison, Lucy Packer; Alex Matthews, Marlie Packer, Sadia Kabeya; Sarah Beckett, Zoe Aldcroft; Sarah Bern, Lark Davies, Hannah Botterman
Replacements: Connie Powell, Mackenzie Carson, Maud Muir, Poppy Cleall, Morwenna Talling, Natasha Hunt, Amber Reed, Jess Breach
Coach: Simon Middleton (ENG)