Klopp committed his future to the Reds by extending his current deal, which was due to expire in 2022, by a further two years on Friday.
It came on the same day that former Gerrard penned an extension with Scottish club Rangers, which will also see him stay at Ibrox until the end of the 2023/24 campaign.
But Dalglish dismissed the development as a coincidence, writing for the Sunday Post: "Steven Gerrard signed a new contract that ties him to [Rangers] until 2024. But spare me the notion it all goes hand in hand for Steven to go to Anfield and replace Jurgen in five years' time.
"Listen, I know it's Christmas time and we all like a good fairy tale.
"However, nobody - including Jurgen, Steven, and me - can look five days into the future never mind four or five years.
"For anyone to suggest otherwise is putting two and two together and coming up with 222.
"So let's get back to reality."