The Reds last defeated the Gunners on North London soil in February 2000 and Dalglish says perhaps this Saturday at the Emirates Stadium could be the match that breaks a 14-match winless run.
"Maybe we're due for a win," said Dalglish. "But it is not going to make it any easier for us because they have lost Fabregas, Nasri is unlikely to be playing and they have a couple of suspensions.
"It will still be a difficult game for us. Arsenal have been most football fans' second team because they play great football and are entertaining to watch.
"Unfortunately they have not won anything for six years and that is the ***** they would love to have off their back.
"But they are still a team I have the greatest respect for and so we go in there and hopefully we can make it as difficult for them as they will for us.
"I don't know how they are going to react, it is up to us to know how we are going to react.
"We can control what we do and we can compete against them - that is all we can do."