Hodgson is out of contract with the Baggies in the summer and is in no rush to make a decision on his future.
Olsson can understand why Hodgson is being viewed as a possible candidate to replace Fabio Capello as England coach but knows how crucial he is to Albion's future.
The central defender said: "I think it is important for the club's development that Roy Hodgson stays.
"I am not surprised he is in the frame as one of the England candidates.
"He is a top manager and has done really well in the Premier League with Fulham and now us.
"I'm not surprised he has been mentioned but I hope he stays here. Everyone at the club is very happy with him.
"I'm thinking he's enjoying himself and hopefully he will come to an agreement with the club."
Olsson believes Hodgson's organisational skills have been a key factor in keeping Albion in the top flight last season and building on that platform this term.
West Brom are currently 14th in the standings following their 5-1 mauling of Wolves on Sunday, eight points above the relegation zone.
He said: "In all the years I've been here, people have seen we can play some really good football.
"But what we were lacking before the current gaffer came was organisation and the shape of the team.
"He is a top coach at bringing that together, maybe the best in England I think, the best I have worked with from that perspective, definitely."
Striker Peter Odemwingie, who scored a hat-trick against Wolves, knows losing Hodgson will disrupt the continuity at The Hawthorns.
He said: "Roy is a big manager and it depends on what he wants to do.
"He has had success here and he has already built relationships with people in the club so he would be welcome (to stay).
"We are getting to know each other and understanding each other collectively as a squad and that is important.
"Everybody knows what to expect from each other and that is a big plus.
"When someone new comes in, you have to start from the beginning so, if we can all get what we're looking for this year, then why change when things are going fine? I hope he stays."
Odemwingie insists his personal working relationship with Hodgson is fine after an exchange of views earlier in the campaign when the player was sidelined with injury problems.
He said: "We are fine and we always were. If we weren't, I would have been talking about leaving the club or something else.
"But he told me that whatever he says can be out of frustrating and not anger.
"He is an experienced person and I have to respect him, my manager.
"Sometimes I felt it was a bit harsh on me, and I said that to him, but he said I shouldn't take it in a bad way.
"He said he was frustrated that I wasn't available (because of injury) and that was it."
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