Downing has been in charge at the Hawthorns since Clarke was relieved of his duties earlier this month.
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"I've always said that I'll be there supporting the best I can until they get the correct one, and in fairness, in the last two or three appointments, they've got the right one," he told reporters.
"I know there's a lot of speculation going around, but I really have just tried to concentrate on the 20-odd players that have come down [to London for fixtures against Tottenham and West Ham] and I've got to focus on what I'm controlling.
"If anybody steps in, I'll gladly support whoever comes in. The quicker we do it the better. But, having said that, it has to be the right one."
Downing led West Brom to a 1-1 draw at Tottenham on Thursday, and is almost certain he will still be in the dugout for Saturday's clash at West Ham.
"As far as I know," he continued. "We've planned for the next two or three days, so we're ready to go.
"West Ham's always going to be a difficult game. We know what they're like, we know their strengths and I'm sure Sam [Allardyce] will have them charged."
West Brom currently sit 15th in the Premier League with 17 points from 18 matches.