Warriors are on the hunt for a home quarter-final, and McBeth has played a key role in the absence of the injured Jamie Bhatti.
With four games left in the regular season, Glasgow are still in the mix to secure home advantage in the play-offs and set up a big opportunity to win the URC title.
That would take the season up until June 22 before Scotland then have a tour of Canada, USA, Uruguay and Chile in July.
McBeth - who has represented Scotland and South Africa at U20 level - is eligible for a call-up due to his Scottish grandfather.
Gregor Townsend is expected to rest a number of first-choice players, giving players like McBeth an opportunity to prove their worth at Test level.
McBeth told scotlandrugbynews.com: 2I'm Scottish-qualified but just taking it game by game just now. I'm just trying to play my best for Glasgow at the moment.
"Obviously, I'm hoping to be on the tour but if I'm not then I'll just do my best for Glasgow and keep the ball rolling.
"I've not spoken to Gregor about it yet but I'd imagine all the chat about it will be after the season. For now we're all just focusing on the URC.
"I've been blessed now to start a few games in a row. That's been very good.
"Franco has helped me and motivated me so I'm very happy to get a few starts under my belt now. I had been benching for a while before that.
"With Leinster losing away to the Lions we're wishing we also took a bonus point against the Sharks. And then we would have been even with them in first place.
"It's going to be tough over the next few games but we have some good momentum, especially at Scotstoun.
"The more games we can get here the better.
"Obviously we have Zebre this weekend and then the two South African games so these are massive games for us.
"We want to end the season as high as possible and play all our games at Scotstoun if we can. The feeling is we have to work hard, play hard and show our dominance."
Competition at loosehead is strong at Warriors and will be further bolstered with the arrival of Rory Sutherland.
The British and Irish Lion will add to depth that includes McBeth, Jamie Bhatti and Oli Kebble, but McBeth says he is looking forward to welcoming Sutherland to the club.
He continued: "I met him once before but he sounds like a great guy so I'm excited to have him here as well. It will be good.
"It's a lot of competition but that's the wonderful thing about this club. We have such great players for the same position and we all push each other and want the best for each other. That's perfect. It's a lucky position that we're in to have so many class players for each position."