Hodgson was replaced by Dalglish in January after overseeing the worst start to a Premier League season in Liverpool's history.
Dalglish has played down their meeting, but Hodgson believes his position was not helped by the fact that the Reds legend openly admitted he wanted the manager's job prior to his appointment, a fact acknowledged by the Liverpool faithful.
“Kenny had made it known he wanted the job and I was appointed. But that’s football, Hodgson told Sky Sports.
“Every time you take a job there can be an icon waiting in the wings like that.
"Kenny and I have never been particularly close friends. I don't know him that well but I have no animosity towards him," said Hodgson.
"I'm perfectly happy to see him in the job and I'm happy to be in the job I'm in.
"I'm not prepared to make any comments personally about any member of staff, let alone the manager."