Carsley named his 25-man squad on Thursday, with no recognised left-back included for the assignments against Greece and Finland.
Luke Shaw featured for England at Euro 2024 but got injured after the tournament during Manchester United's pre-season while Chelsea's Ben Chilwell is struggling for regular game time.
Levi Colwill and Rico Lewis, who are not traditional left-backs, filled in at the problem position during England's last round of international fixtures against Ireland and Finland.
They stand a likely chance of reprising their roles against Greece and Finland, but Carsley refused to rule out using Palmer, Trent Alexander-Arnold or Bukayo Saka at left-back.
'Yeah, he (Alexander-Arnold) can play there,' Carsley said.
'Bukayo can play there, Cole can play there, so there's quite a few. Obviously you want to get the best out of them in their most natural positions.
'We know if we play a right-footed player there, at left-back, that we're going to have to build differently and be creative in the way we set up, I think if you're asking a right-footed player to play high and wide and playing too high and wide, it can be sometimes a little bit predictable.
'It's important that we aren't predictable, that we've got different ways of attacking and I think with the players we've got we can also swap the players over the wide players so they are on their natural sides just to give the opposition something different to think about.'
Saka began his Arsenal career at left-back before he transitioned into his role as one of the best right wingers in the Premier League.
As for Alexander-Arnold, he has almost exclusively featured at right-back throughout his club career at Liverpool, with some cameos as a central midfielder and higher up the right flank.
However, Carsley's mention of Palmer as a left-back option is the most surprising given he has become a household name due to his exploits for Chelsea as an attacking midfielder or out on the right wing and cutting inside.
According to Transfermarkt, Palmer has not featured once at left-back throughout his club career, going as far back as his time with Manchester City's Under-18s.
The 22-year-old has started the 2024-25 season in tremendous form, scoring six goals in as many games along with four assists.
Four of his goals came in a man-of-the-match performance against Brighton last Saturday, including a stunning free-kick from 35 yards that left Seagulls goalkeeper Bart Verbruggen with no chance.
Palmer even had the audacity to pull off a Panenka from the penalty spot to underline his calmness under pressure.
Despite his blistering start to the season, Palmer is not guaranteed a spot in his preferred position in the England line-up with Phil Foden and Jude Bellingham in the squad.
Carsley felt trying to squeeze the trio into his team was a 'nice problem to have' but conceded he would have to get 'creative' to do so.
'You'd try and find a way of getting them into the team,' Carsley said.
'We've got to be creative... if they are all playing well and they earn that place in the team. I think that's important as well.
'With the period of the season we are in, I can probably justify why we wouldn't start all three of them at the same time in terms of the amount of games that they're playing, what they are going back to and what they have come from.
'And some of the stages they are at in terms of potentially just coming back from injury or not had that many minutes. We just need to find the right balance.'
Carsley's audition to become England's permanent manager continues against Greece on October 10 and Finland on October 13.
