Pressley is close to agreeing a move to npower League One side Coventry after leading the Bairns to the semi-finals of the William Hill Scottish Cup.
Smith and assistant manager Stevie Crawford are now expected to take the team for Saturday's trip to Irn-Bru First Division leaders Morton.
And the 73-year-old - who has twice won the Scottish Cup with St Mirren and Aberdeen - says he fancies a third shot at the trophy and could even be persuaded to take the job on a full-time basis.
But Smith conceded that Falkirk chairman Martin Ritchie may decide to place his faith in youth once more and hand the reigns to Crawford, 34 years his junior.
Falkirk face Hibernian in their Hampden semi on April 13.
He told Press Association Sport: "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.
"We have got a big game at Hampden and the rest of the league programme too, so there is a lot going on.
"But Stevie Crawford has also stayed on and being an ex-manager with East Fife himself, the club might decide to give him the opportunity."
Falkirk granted Pressley permission to talk to Coventry City just days after the former Scotland defender led the Bairns to the last four of the cup with a 2-1 win over Hamilton.
He now looks increasingly likely to succeed Mark Robins, who left the Sky Blues to join Huddersfield Town three weeks ago.
And Smith believes his 39-year-old apprentice has got what it takes to lead the fallen giants back up the English football ladder.
He said: "I hope Steven is a success down there - he's got everything you need to be a success.
"If he gets the backing and the finances, he will be fine. He's a very promising manager."