The former England boss, 75, confirmed last week that he is terminally ill and has one year to live “at best”.
As part of his interview with P1, he revealed that he is a lifelong Liverpool fan and regrets never being able to manage them professionally.
That caused Liverpool fans to launch a petition for Sven to manage the Reds in an upcoming charity match in March.
The game will see Liverpool legends take on Ajax legends, and he was asked about the offer on Good Morning Britain today.
Asked if he was aware of the petition, he said: “No, I didn’t know about that. I knew that I had a charity game in March, I think it is, and me and my son are invited to see that game and that might be great.
“There will be a lot of good football players there, but I should be their manager? No, I never heard that, I don’t know where that’s come from.
GMB host Susanna Reid then asked if he would accept the role and he said: “I would accept, of course.
“To coach Liverpool, that would be my dream. That’s always been my dream but I’m not complaining, I had a lot of good football teams, national teams and clubs so I’m happy.”
Some of Eriksson’s former club teams include Lazio, Benfica, Manchester City and Leicester.
He led England for the 2002 and 2006 World Cup as well as Euro 2004.
Eriksson has revealed that he want to live the rest of his life positively and lead an “as normal” life as possible despite his terminal diagnosis.
He explained: “I have a lot of friends here in Sweden, of course, they’re coming to visit me.
“I go out, having a coffee with them, a lunch with them, things like that. I try to be normal. I’m travelling a little bit less than I did before, but I’m still travelling.
“I hope to come to England maybe to see England Brazil in March, that could be a game in the final of the World Cup but it is a friendly. We’ll see but I’m not complaining and I refuse to sit down and cry, feeling sorry about myself.”