Albion are reportedly keen to take Sinclair, who joined City from Swansea last summer but only made three starts, on a season-long loan.
Asked about the 24-year-old on Thursday, Clarke said: "I know there was initial contact between the clubs and I know there has been continued contact between the clubs.
"Beyond that, I don't know if we are close to a deal or if we are far away from a deal.
"There are still talks ongoing at this moment in time."
Clarke has already completed permanent signings in striker Nicolas Anelka and defender Diego Lugano this summer, as well as recruiting Udinese frontman Matej Vydra and Dynamo Kiev full-back Goran Popov on loan deals.
On the possibilities of further additions before the end of the transfer window, Clarke said: "At the moment, if I could get two more in, I'd be happy.
"And if I could get three more, then I think we'd be set. I'm staying confident."
But it seems former Chelsea forward Salomon Kalou will not be returning to the Premier League from Lille.
"No, I think that one is dead," Clarke said.