Palmer was one of the best players in the Premier League last season and has continued his sensational form this term, scoring six goals and making five assists in seven games.
The 22-year-old had more goal involvements than any other player in the Premier League last term and his form saw him win the Young Player of the Season award.
Already on a seven-year deal following his £40m move from Manchester City, Palmer signed a contract extension at Stamford Bridge in August, hypothetically keeping him at the club until the summer of 2033.
Whether he actually stays at Chelsea for a decade remains to be seen and Souness believes he could emerge as a target for Real Madrid next summer.
‘I’m sure there are other players Man City could have cashed in on,’ Souness told the Daily Mail.
‘Chelsea paid £40m for Palmer but if Real Madrid come knocking next summer and he is still at the level he is showing, I would not be surprised if they got an offer of £150m for him.
‘He’s a young man, so we’re going early on this call, but if this is Palmer’s level and he can be consistently this good, he’s going to be a top man.
‘He has got silky skills, athleticism and a fabulous football brain. There’s simply nothing to dislike about him. He’s 22. At that age, no one ought to be that good.
‘I like his temperament, too. You can read a lot into a player from their reaction when they score, and Palmer doesn’t go mad when he finds the net.
‘He seems to have a really sensible head and he looks to have had a really good football education – which you would expect at the modern Manchester City.’
Palmer’s goal contributions this season were mainly assists before he became the first player in Premier League history to score four first-half goals in the 4-2 win over Brighton at the end of last month.
Following Palmer’s four-goal heroics, Manchester United and England legend Gary Neville admitted he had been ‘completely shocked’ by the Chelsea star.
Asked whether he rated Palmer as the best player in the Premier League, Neville told NBC Sports: ‘He’s not far off! I have to say that I was surprised last season.
‘I remember when Mohamed Salah scored those goals all those years ago and I thought, “He won’t repeat that in the second season, he won’t repeat that in the third season”, and Cole Palmer is just going and completely shocking me in terms of what he’s delivering.
‘I can’t believe the level that he’s getting to and to think that he wasn’t playing for England in the European Championship in the summer now just seems absolutely ridiculous.
‘And it seems even more ridiculous that Manchester City, who have been unbelievable in the transfer market, have let one of their own go.’
Palmer made yet another assist at Stamford Bridge on Sunday in Chelsea’s 1-1 draw with Nottingham Forest.
The visitors, who were reduced to ten men late on, took the lead shortly after half time through Chris Wood before Noni Madueke equalised for Chelsea.
Following the draw, which leaves Chelsea fourth in the Premier League going into the international break, Blues boss Enzo Maresca said: ‘I think we deserved to win.
“They are a very good team and we knew they would defend well. It was a tough and tricky game, very different to Brighton. We were patient on the ball and created chances.
‘Overall the performance was good and I think we deserved to win. Their keeper was the best of the game. We created chances and arrived at goal in the way we want to.’
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