Pressley, who has led Falkirk to the semi-finals of the William Hill Scottish Cup, is close to agreeing a move to Coventry City.
Smith, along with assistant manager Stevie Crawford, is now expected to take the team for Saturday's trip to Irn-Bru First Division leaders Morton.
He told PA: "Steven has one or two things to tidy up with Coventry, but I think he will be on his way.
"So, I will be taking things with Stevie Crawford this weekend and we'll take it from there. I wanted to help the club and I expect we will go along on this basis until the end of the season.
"If the club were to ask me to take over on a permanent basis, that wouldn't be a problem for me. When you are a manager for a long time like I was, you do miss certain things when you give it up. Things like the big decisions."
Smith, 73, has twice won the Scottish Cup during managerial spells at St Mirren and Aberdeen.