Gemmill will have to do without both players for the forthcoming European Under-21 Championship qualifier against Andorra but is confident they are up to making the next step in global football.
Gemmill named his squad for this month's European Under 21 Championship qualifier with Andorra on Tuesday.
McBurnie has scored five goals in seven appearances since joining Barnsley on loan in January, having made a number of Premier League appearances for the Swans.
He said: "He's shown it, he's selected some of them in his first squad since coming back in the building, he's made it clear he's putting a real interest in not just the Under 21s but the 19s and 17s".
"There's a big thing to play for this club but so far he's on a great track, he's given himself the best possible chance to fulfil that".
There is no doubt that on his day the 25-year-old midfielder is one of the best players in Scotland, but the surprising factor is that the player is only just back from injury after nearly two months out with a hernia injury.
England had tried to persuade the young central midfielder to represent them rather than Scotland but failed despite him not representing either country at any youth level.
"It is a real motivation for all the players to continue their progression".
"Peter has been with the 21s all year and was at the Toulon Tournament last year (with Under-20s), so it has really helped his knowledge of the younger players", said Gemmill, who was "extremely flattered" to be linked with the Scotland post before McLeish was appointed for the second time.
As Gemmill, who has never managed a club, sat down yesterday to announce his squad for the...
He added: "It was enormously flattering, there's a huge interest in the national team".