Scotland winger James Forrest says Celtic team-mate Scott Brown is a "great leader" and that other players will now need to fill that role with the national squad.
Brown announced his retirement from international football for a second time, having earned 55 caps.
"He will be missed, but there will be other boys that think they can make the step up," Forrest said.
Rangers manager Graeme Murty has urged his midfielders to fill the gap.
Murty, who thanked Brown for his international service, challenged Ryan Jack, Greg Docherty, Graham Dorrans and Ross McCrorie to establish themselves in the national team.
"He (Brown) has been a really, really good servant. He's taken fantastic care of his body and you see that the impact he has on his team is very big," Murty said.
"It's now up to someone else to fill the hole that he will leave. It's an opportunity - possibly for some of our players - to make that midfield role their own.
"So as a Scotland fan I would thank him for his work but there is an opportunity to move forward now with a group of players that are working with a new manager to try to stake a claim and play in his team."
Forrest, who describes Brown as a "huge influence" on his career, made his Celtic debut in 2010, three years after Brown joined the club.
"Broony's done tremendous when he has been captain and [with] what he's done for Scotland. But it opens the door now for someone to step up and take charge.
"Being in Scotland squads before, there are definitely a few characters in there and captains from clubs as well, so there are definitely a few options."
Scotland face friendlies against Costa Rica and Hungary at the end of March, and McLeish will now have to think about who will captain the side when he picks his squad early next month.
The pair have won 12 trophies for Celtic in that time, and Forrest says that after he graduated from the club's academy, Brown's personality and mentoring helped him make the step up.
"When I came through with Celtic he took me under his wing, the same with Scotland as well - he's always been there," Forrest said.
"He's great for young boys coming through, he makes them feel a part of it, but also makes them work hard as well.
"Obviously he was really good for me coming through with Celtic. He's really good with young boys as well. Just the way he is about the place, he makes everyone feel welcome.
"For boys coming into the Scotland squad for the first time he gets everyone together. He's been great for me and my career."