The 26-year-old has a year left on his current deal, and even though they have an option for an additional 12-months - the club are looking to tie him down to a new deal.
The Baggies have successfully persuaded the likes of Jonas Olsson and James Morrison to sign new long-term deals in recent months and Clarke hopes Mulumbu will be next.
"Youssouf has been excellent for us since I have been here and is one of the players we want to keep," said Clarke.
"I think come the summer the ones that we have to keep - that I want to keep - will still be at the club."
Fiorentina are one of the clubs linked with DR Congo ace, who joined the club from Paris Saint Germain in 2009.