The Pittodrie side's achievements in reaching the League Cup final, knocking Celtic out of the William Hill Scottish Cup and climbing to second place in the SPFL Premiership - have led to suggestions that the likes of Mark Reynolds, Peter Pawlett and perhaps goalkeeper Jamie Langfield might find their way into Gordon Strachan's Scotland squad for the friendly against Poland in Warsaw on March 5.
Meanwhile, Willo Flood is said to have caught the eye of Roy Keane, assistant to the Republic of Ireland manager Martin O'Neill, at Celtic Park last weekend.
However, McInnes, the Aberdeen manager, said: "It's nice to be recognised in international football but I'm not going to be pushing it. The national team managers know what they need and know who is out there. I'm not one for banging the drum.
"We have good players here and players get highlighted when they're part of a successful team. Hopefully, if we can be successful this season it will help their cause. It's not for me to tell the international managers what to do but I'm sure there will be a few more being looked at than were at the start of the season."
On Flood specifically, McInnes added: "I'm always wary of club managers pushing their players too much for international honours and I don't know the strength in depth of the Republic of Ireland.
"But if you're asking me about the credentials of Willo Flood as a footballer, he has been such an important signing for me as a manager.
"He brings a consistency of performance, he brings an attitude to the team, he brings a personality to training every day, and he brings a real mentality to the whole club. Any manager is drawn to that type of player.
"He has good feet and he chips in with the odd goal but he always brings a level of performance. When Willo Flood is on your team sheet you know exactly what you're going to get.
"If he's part of a successful Aberdeen team, which we hope he will be, then he and a few others might just be able to get the opportunity to be in international managers' thoughts. If they have been watching him of late, they will only have been impressed."
McInnes's "one game at a time" mantra is unwavering and his focus yesterday was on tomorrow's league encounter with St Mirren in Paisley.
While Aberdeen produced a blistering display to beat the holders last weekend, Danny Lennon's team went down 2-1 to Dundee United at Tannadice in their Scottish Cup tie.
McInnes challenged his players to bring the same intensity to the game as they did against Neil Lennon's men. "They have to take confidence from those sort of results but must recognise at the same time that just because you beat Celtic and win a semi-final, it doesn't mean victory be automatic against St Mirren," he said.
"There's a challenge there, 11 players from their team trying to stop us winning, and we have got to be ready to go toe-to-toe with that. The same motivation has to be there."
McInnes cited comments made by Adam Rooney, the former Inverness Caledonian Thistle front man who joined Aberdeen last month, as displaying the type of hunger he wants from his squad.
"Even though we won last week the first thing Adam said to me was that he should have had three goals in three games," McInnes added. "I like that attitude in a striker. "There's a selfishness to playing in that position; all the top forwards have that streak in them. He's certainly a player who will help us going forward."