Former Rangers defender Danny Wilson and ex Hearts winger Sam Nicholson, who both play for Colorado Rapids in the United States, are being considered as emergency recruits after Stuart Armstrong and John Souttar became the latest players to call off from the trip.
McLeish concedes the squad is “getting quite thin” for the games against Peru, which kicks-off in the early hours of Wednesday morning, and Mexico on 3 June.
With travel now an issue – the Scotland party takes off tomorrow for Lima from London, via Houston – McLeish has been forced to be practical when assessing his options.
The withdrawals of Armstrong and Souttar take the total calls-offs to six since the Scotland manager named his squad at the beginning of last week.
Matt Ritchie, Barry Douglas, Ryan Fraser and goalkeeper Allan McGregor had all already pulled out.
Motherwell’s Chris Cadden, Kilmarnock’s Stephen O’Donnell and Celtic goalkeeper Scott Bain have been added to the travelling party in the last few days.
Johnny Russell, now with Sporting Kansas City, is already in the squad but won’t catch up with his team mates until they arrive in Mexico City.
Attention has turned to Wilson and Nicholson, Russell’s fellow Stateside-based Scots.
Wilson, who left Rangers for Colorado Rapids midway through last season, already has five Scotland caps. Nicholson has never been capped at full international level but played for the Under 19s and Under 21s.
He joined Wilson in Denver earlier this month after a year at Minnesota United FC.
The only other Scot currently playing in Major League Soccer is 28-year-old midfielder Calum Mallace, who plays for Los Angeles FC. He moved to the States from Scotland as a young boy and has never been capped at any level.
“We (already) have Johnny Russell – he will miss the first game (v Peru) but he will come and play in the second game,” said McLeish. “There’s a couple of other Scottish boys out there who have good experience we can maybe call upon.
“We have not made that fitness for duty call yet but that could be on cards,” he added. “We will assess things in the morning.”
One obstacle could be Colorado Rapids’ own league games scheduled for this Sunday against Portland Timbers and the following Saturday against Vancouver Whitecaps. They are currently bottom of the Western Conference.
McLeish dismissed the sceptics questioning the extent of Souttar and, specifically, Armstrong’s injuries. The Celtic midfielder sustained a hamstring strain in the 18 minutes he was on the field in his side’s 2-0 win over Motherwell in Saturday’s Scottish Cup final.
“Stuart has a little tweak in his hammy,” said McLeish. “He flagged it up right away after the game. I believe it has been scanned.
“We are obviously waiting on the results of the scan. He is not going to make it. He genuinely wanted to come.
Souttar, meanwhile, has a problem with his hip joint sustained in Hearts’ recent 3-1 defeat to Celtic. “The kid was gagging to play,” said McLeish, who stressed the need to remain philosophical about the latest unwelcome developments.
“Teams that are not in the World Cup don’t have to send their players – I am not sure if you are aware of that,” he said.
“Sometimes managers can rage and say: ‘Well listen, we are still wanting to do a medical with them’. But we have to trust in the clubs and we have to have a rapport with the clubs.
“That has definitely got to be an on-going thing. It has been very difficult at this particular time with the end of the season and players playing on injuries in the last few weeks.”