But McLeish will focus on the goalkeepers available to him as he ponders his new number one following Allan McGregor's sudden international retirement.
Current Celtic first-choice keeper Scott Bain, Millwall goalie Jordan Archer and Sunderland's Jon McLaughlin are in the squad for the Euro 2020 qualifiers against Kazakhstan and San Marino later this month.
But Gunn remains on Scotland's radar and McLeish has a strong connection to the former Manchester City trainee through his father, Bryan.
Gunn senior played with McLeish at Aberdeen before travelling south to Norwich after failing to dislodge Jim Leighton, who helped the Dons to European glory in Gothenburg in 1983.
Gunn junior, 23, has featured for England Under-21s and has made 10 appearances for Southampton since his big-money summer switch, so playing for the land of his birth appears to be his priority.
McLeish said: "I've been in constant dialogue with big Bryan Gunn for over a year, one of the Gothenburg guys.
"We have a Gothenburg group and the other players tease him about it, then I have to send a private (message) saying 'Does Angus want to play for Scotland?'
"But I don't really want to talk about guys who are not available to us at the moment, and get right behind the three goalkeepers we have, who are all terrific players.
"There would be no guarantee Angus would walk into the number one spot. He is still going through a maturity process, being at Norwich on loan from Man City and then getting a fantastic move. That must have empowered him.
"He would think he can now rise to a different level, but our three goalies have been playing regularly, and playing to a very good standard."