Clark was the surprise hero in both boxes as Saints dumped Rangers out of the Scottish Cup quarter-finals on Sunday.
He pulled off a string of saves - including two in the penalty shoot-out - and also played a key role in Chris Kane's extra-time equaliser after darting forward for a late corner.
The 28-year-old has long been tipped for a Scotland cap but has so far not received a call-up.
But Davidson reckons Clark and Saints captain Jason Kerr could yet force their way in if they can hold their nerve again and double up on this season's Betfred Cup triumph.
"For me, what Zander has done this season is produce in the big games," said the Saints boss.
"You look at the Betfred semi-final against Hibs, he produced some top-class saves and one in the final as well, all at really important times.
"On Sunday night he was absolutely superb too when we needed him to be. So for me he's playing the big games well. That's all he can do.
"It's up to the Scotland manager but it's great to have a young Scottish goalie with such a big presence. Hopefully in the big games his form can continue. Is he good enough for Scotland? Yeah, without a doubt he is.
"When he first broke through at St Johnstone, his issue was consistency. Now he's producing those types of performances consistently. He's good with the ball at his feet and he's a great size so he ticks a lot of boxes.
"It's just about him playing well in the big games and showing the mental side of the game, which for me he has done, and hopefully he will get an opportunity.
"Jason is the exact same as Zander. I've worked in the national set-up with Gordon Strachan so I know sometimes how fickle it can be for squad selections.
"All I'll say for Jason is it might come a bit early for him. Over the season - especially the last three months - he's been one of our best players.
"That's credit to him. Can he force his way in? The better you play in the bigger games the more chance you have of getting into the squad so hopefully we can make the final and give Steve Clarke the chance to have a good look at them."
The prize for knocking out Steven Gerrard's Premiership winners is a semi-final showdown with St Mirren a week on Sunday.
St Johnstone won a narrow race to pip their Paisley namesakes for the top six earlier this month and Davidson expects the last-four clash to be another tight affair.
"The Rangers game was a huge one for us - no-one gave us a chance," he said. "Now it's opened the whole tournament up.
"There's some really good teams left in it but all we've done by beating Rangers is give ourselves a chance. Now we need to compete well in the semi-final.
"We sneaked past St Mirren on goal difference to get the top six so that shows how close it's going to be."