Heckingbottom has only won two of his 13 games in charge at Elland Road, having replaced Thomas Christiansen as manager in early February.
And some fans are already calling for a change at the helm next season, with McCarthy - who is the current bookies favourite - a popular choice after leaving Ipswich Town earlier than planned, this month.
Asked about Heckingbottom's situation at his former club, Palmer told Proper Sport: "It was always going to be difficult for him when he came in.
"I’ve seen Leeds a lot this season and the squad’s not got the right make-up. They’ve got a lot of foreign players in the side and it’s not the right make-up to compete in the Championship - not for me.
"The problem that Paul’s (got) is that those players are there and on long-term contracts, it’s very, very difficult. I know he’s tried to shuffle the pack, he’s tried to move it all about.
"I don’t know what he’s like with the chairman and whether he’s turned round to the chairman and said, ‘right, listen: what I need to do now until the end of the season is see what I’ve actually got by playing all these different players? Can I clear these players out and can I bring in these players?’
"I don’t care who is in there now, they would have had a problem between now and the end of the season. It’s difficult for managers when they come into the football club because it’s a results-based industry.
"But if you’re talking about the long-term strategy, which is to get promotion to the Premier League, he needs to have a look what’s available and say, ‘listen: this is where we need to change. Four or five players need to go. Can we bring these other players in?’
"Mick McCarthy would have a problem with the squad at Leeds United, he would need to overturn that. But let me tell you, any club that gets Mick McCarthy have done very well."
Excluding this one, McCarthy completed five seasons at Ipswich, in which he achieved three top-half finishes - making the play-offs in one of those - despite a tight budget.
The 59-year-old - whose CV contains two promotions - has admitted on several occasions to being a boyhood Leeds fan, with an affection too for hometown team, Barnsley.
However, he has since insisted that he only has eyes for the Tykes - although that didn't prevent Heckingbottom from moving between the two.