The 24-year-old is nearing the end of his current deal with the Rams, but Clough hopes to agree an extension with West Brom.
"We want to try to keep him here until the end of the calendar year," said Clough in the Derby Evening Telegraph.
"He's got two more games until his second month is up and then we could extend it until December 31, which would take us up to the maximum of 93 days."
Clough added: "Luke is our No 1 striker at the moment, when he is fit.
"He was a little bit short of fitness at Leicester after about three weeks out injured. But he will get stronger and fitter with each game now."