McLeish will lead out the Scotland team on Saturday at Hampden in Scotland's final Group B Euro 2008 qualifying match against Italy.
If the Scots win, they will be guaranteed a place at the finals next year in Austria and Switzerland.
However, Smith said there would be no rush to renegotiate McLeish's contract, but is hopeful that he would still be in place should Scotland qualify for the finals in 2008.
"We very much hope Alex stays in place and depending on what happens over the next weeks and months we will certainly be looking at extending his contract further," said Smith.
"But right now I'm assuming he would be here for the finals if we make it.
"Alex is under contract and very committed."
Meanwhile, McLeish remains confident that Scotland can give a good account of themselves against Italy in the crucial qualifier.
"I think back to the World Cup and how Australia and USA played against Italy and I take great optimism from both games," said McLeish.
"There's no doubt Italy are beatable and we are capable of winning.
"France defeated them in this section and we have beaten France, home and away.
"That also gives us confidence."