The Boys in Green host Switzerland at the Aviva Stadium on Friday night before facing Slovakia at home on March 29.
Judge, who has 14 goals in 34 appearances this season, has been told he will probably be handed his debut in one of those games and Smith believes it would be a proud moment for Brentford.
The head coach said: “It'd a proud moment for the club but only because of how Alan's career has gone.
“I remember playing against him when I was in charge at Walsall. It's great so see people rise up through the lower leagues, establish themselves in the Championship and push for international recognition.
In pictures: Alan Judge's remarkable season
“He'll deserve it when he gets there because he's done it the hard way. He'll go and enjoy it and give it his all. I think he'll go and do well.”
Judge has, at times, shown his frustration on the pitch and has displayed a selfish streak on occasions and Smith has spoken to him about it.
He added: “I think Alan gets frustrated as he knows how we can play and I think he takes it upon himself sometimes as people expect him to score.
“Alan knows how important he is to the team and how important the team is to him. He's brilliant to have around the training ground.”