Thompson won seven league titles, three European Cups and the FA Cup with the Reds as a player during the Merseyside club's golden age of the 1970s and 1980s.
Jurgen Klopp has led Liverpool into a strong position to win their first league title for 29 years this season and, ahead of their clash with rivals Manchester United on Sunday, Thompson said his former club have Premier League rivals trembling with fear.
"A lot of fans are worried about the cycle coming around again, not just Manchester United," Thompson told Sky Sports News.
"They are frightened. That's why they are starting to get nervous of Liverpool winning the Premier League again.
"A lot of people don't want it like the '70s and '80s again and a lot of people wouldn't want Manchester United to do it again."
“It's been far too long. The Premier League has become the holy grail and maybe even the burden for too many years.
"But it would be the pinnacle, and if Jurgen Klopp was able to pull it off in these days of the big money Manchester City and Chelsea have thrown at it, it would be quite unbelievable.
"Yes, we got to the Champions League final last year - we didn't win, but what a wonderful occasion it was - and we remember 2005, but give me and most Liverpool fans the Premier League any day."
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