Hodgson, who was appointed manager of the south London club in September 2017, is out of contract in the summer.
However, Parish is confident the 72-year-old will prolong his stay at the club with both parties relaxed about the situation.
He told Palace TV: "Yes, we have presented an offer to Roy and we are talking to him about that.
"I think everyone is pretty focused on the games, but yes that is in discussions and for Roy, he has said himself in the press that he is very relaxed about it.
"We are very relaxed about it I think, and we'll get that done in the fullness of time."