The former Fulham boss is fretting over making a first phone call to the Manchester United chief since being unveiled on Merseyside on Thursday.
Liverpool and United are arch-rivals and Hodgson fears that it could put a strain on his friendship with Ferguson.
The Reds boss said: "I know Sir Alex is not really a Liverpool man so I'm a bit concerned about my excellent relationship with him.
"I hope he forgives me for moving north and, hopefully, we can have a glass of wine together, maybe in secret.
"I hope that's how he is going to see it but he is one of the people I intend to ring to find out.
"When I rang the Fulham chairman to say I wished to move to Liverpool, that was one call I had to get out of the way and Alex might be the next one.
"I must say I've always believed you don't have battles with other managers.
"Football teams have battles with other football teams, clubs have battles with other clubs and I've never subscribed to that theory that it's me and you.
"I used to find it quite ridiculous in Italy when they used to compare your record against another manager. It's a nonsense.
"If you happen to be manager of a club who is fighting for survival against a club which wins the title every year, the chances are that in the battles you've had he's won one and you've won five. That's the way it goes."
Meanwhile, Hodgson has indicated that he will be prepared to offer fringe players in his inherited squad the chance to impress.
He said: "Whenever a new manager comes in, players who have been on the periphery start to see it and maybe think, 'this could be my chance, I'll have a go'.
"You'd be foolish as a manager not to give them that chance."