Hodgson, now in charge at West Bromwich Albion, has his first chance to exact revenge for his sacking on Saturday when Liverpool visit The Hawthorns.
"Roy hasn't got anything to prove to anybody," said Dalglish. "If you say he has extra motivation then you are doubting the man's integrity and implying he never had enough motivation before.
"It's Liverpool versus West Brom and we'll face a team that has been prepared by Roy. I don't have a problem with that. It'll be nice to see him again."
Hodgson's six-month spell at Anfield ended in January after 31 games in charge, making him the most short-lived appointment in the club's history. He was hired by West Bromwich in February, replacing Roberto Di Matteo, and his new club are unbeaten in his four games in charge.
"Roy brings his own management style to the club and they have done well since he went in there. We are looking forward to the game. I have great respect for him, as I said when I came in here, and that isn't going to change now that we are playing against each other.
"So for me, the game is about Liverpool against West Brom and that's the way I'll go into it. I'll see an old friend of mine standing in the opposite dugout. Everyone knows he's an excellent coach so we know what to expect. We know how they will play so it's up to us to be better than them on the day."
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