David Moyes's side finished above the Reds in the Premier League last season and have started better than their fierce local rivals this term, but former Liverpool manager Dalglish says that the theory that Everton are now the bigger team is not one he subscribes to.
"A lot of people have even been saying that this season could mark a changing of the guard on Merseyside, with some predicting that Everton are going to take over from Liverpool as the top club," said Dalglish in his column in The Mirror.
"Sorry, but I don't see it happening. They finished one place above Liverpool last season but we beat them twice in the league, won the Carling Cup and beat them in the FA Cup semi-final. I think they'd have swapped their season for ours.
"And this season, it's too early to tell."
Everton have not won a Merseyside derby since a 2-0 victory at Goodison Park in October 2010.