David Hopkin, the former Livingston Bradford and Morton boss, is the bookies´ favourite to replace Mark Kerr, who was sacked when Smith took over as owner and chairman last month.
The Championship club, seventh after a 0-0 draw with Raith Rovers tonight, have interviewed a number of candidates but Smith is giving nothing away.
He said: “I’d like to think we’d be in a position to announce it on Thursday. We’re relatively well down the road.
“It’s been a tough couple of weeks. The responsibility has weighed pretty heavily on me this week.
“It’s a big decision. I’m a fan and I know how important it is to the club.
“I was blown away by the number of candidates we got and the calibre. But we set a criteria of what we needed and we are sticking to it.”