The 29-year-old was a fans favourite in his two seasons at Derby at was voted their Player of the Year in 2006 before returning for a second spell at Watford.
Clough is eager to sign the tricky forward before Thursday's deadline for emergency loan deals but concedes Smith may opt to stay at cash-strapped Pompey with the prospect of playing in an FA Cup semi-final next month.
"We've made an inquiry to Portsmouth," Clough told BBC Radio Derby. "But it's a bit difficult with the situation down there at the moment. It's one we'll keep pursuing."
He added: "As soon as we make the inquiry, he goes and plays and scores. The major snag is the FA Cup, which I'm sure he'll want to be involved in. We made an inquiry last week and we've been trying to get in touch with the agent, the administrators and the manager to see if Tommy wants to come or not."