Congo international Mulumbu, who was sent off during Saturday's 3-1 defeat at West Ham, is currently contracted at The Hawthorns until June 2015.
Clarke says the club are looking to tie the 26-year-old down on a longer deal, as well as defender McAuley and striker Long, whose deals both expire next summer.
"We are speaking to Youssouf, Shane and Gareth about new contracts," said the boss.
"Youssouf has been excellent for us since I have been here and is one of the players we want to keep."
Clarke says there are several other players who the club intend to speak to over new deals and is hopeful of keeping his squad intact.
He added: "There are one or two others behind them as well (to hold talks with) but we can't speak to everyone at the same time.
"I think come the summer the ones that we have to keep - that I want to keep - will still be at the club."
Clarke revealed Mulumbu has apologised after lashing the ball in frustration to earn a stoppage-time sending off against the Hammers.
He added: "It is an internal disciplinary matter.
"Youssouf was very apologetic. I think you could tell it just came from sheer frustration at the disappointing performance.
"It is out of character. I have never seen anything like that from Youssouf in the time I have been at the club. He let himself down but he knows that and apologised."