Hodgson's current contract at the Hawthorns expires in June and there has been no indication as to whether he will sign a new deal.
The former Inter Milan and Liverpool manager has been the subject of speculation linking him as a candidate for the England role as Fabio Capello's successor.
Downing said: "Roy has kept his cards close to his chest and I respect that. He's got a lot of things to wait on, I think.
"No-one has questioned it, staff-wise or player-wise.
"Ultimately he's still planning ahead. I don't think he has taken his eye off the ball at all. I think he's still planning for the future here."
Downing has echoed the sentiments of skipper Chris Brunt in believing it is crucial Hodgson remains to help the Baggies become established in the Barclays Premier League.
Downing said: "I do think it is important the club keep Roy.
"We're in the second year in the Premier League and, although we are not safe yet, it's looking good.
"There has to be a structure with a purpose to move on to another level and Roy's experience is vital."