Lee Carsley said England deserve "a world-class coach" as their next manager and conceded he "is still on the path to that".
But the interim boss insisted it was "definitely" wrong to say he has ruled himself out of the running for the permanent job and he is still keeping an "open mind".
Carsley was placed in interim charge of the England senior team after Gareth Southgate stepped down in July, two days after England's Euro 2024 final defeat by Spain.
The 50-year-old took on the role before England's Nations League games "with a view to remaining in the position throughout autumn", while the Football Association continued its recruitment process for a new head coach.
Carsley has not confirmed he is in line for the permanent position, but after Thursday's loss to Greece at Wembley said he would "hopefully be going back to the U21s" - where he was head coach before moving up to cover the senior team.
After England's 3-1 win over Finland, Carsley again distanced himself from the suggestion he hopes to stay with the senior squad permanently.
"I keep saying the same thing. My remit was six games and I'm happy with that," he said.
"This is a privileged position. Really enjoying it but I didn't enjoy the last two days. I'm not used to losing in an England team, I don't take losing well.
"People are always going to try and put their chips on one side. I'm in the middle. My bosses have made it clear what they need from me.
"This job deserves a world-class coach that has won trophies and I am still on the path to that."
Carsley was then asked in his post-match press conference about those comments and if they meant he was out of the running for the full-time job.
"Definitely not," he said.
"The point I was trying to make is that it is one of the top jobs in the world. I'm not part of the process but it deserves a top coach. The players we have available, we've got a real chance of winning. That was the point I was making.
"It was the fact that this is a world-class job. This will be up there with the best jobs in football.
“Whoever gets it is going to be at a high level. It is a privilege to do this job and I feel really well trusted.
"That's why it was so tough the other night to lose the game and have a defeat. The response has been good."
Carsley said he speaks to FA technical director John McDermott - one of the people in charge of the recruitment process for the manager's job - every day but does not ask for updates on the process to find a replacement for Southgate.
Carsley was previously caretaker manager at Brentford, Birmingham City and Coventry, and says the experience of those roles is why he doesn't want to publicly say whether he wants the England job.
"I'm definitely reluctant because in the past when I have done this caretaker or interim role I have gone so far down the 'I don’t want the job', I've actually not done the job," he said.
"It was one of the things I spoke about when I was asked to take temporary charge - it's important that I keep an open mind because in that case, then I'm not being reckless with my decisions.
"I'm thinking thoroughly about how the team should play, the squad I should pick - which is a challenge."
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