Cleary, who is named to start at halfback again for the Blues in the opening game of the 2023 series - which will be played on Wednesday night - has been battling an infected tooth.
The scare for the Blues came after a pair of previous problems, with prop Payne Haas recovering from an ankle issue at training last Friday, and Latrell Mitchell ruled out after suffering a calf strain.
It was ultimately Mitchell's injury which brought Burton into the squad as the new 18th man, with the Canterbury halfback on standby should Cleary need to pull out over the infection. If he does, Burton will play from the bench, with Cronulla Sharks' star Nicho Hynes, who is currently named on the bench, moving into the starting side.
Gould said in his role getting Burton to Adelaide, he was asked to expedite the process, with doubt lingering over Cleary and Brad Fittler wanting to have Burton on the training paddock for the team's final session prior to the captain's run alongside the remainder of the spine.
“If it is infection and the infection runs through his system it can be quite serious, but the extent I don't know,” Gould said on Channel Nine's 100% Footy.
“I said ‘why is it so urgent we get him on that flight and not the next one?'
“He said ‘look, Nathan is in some doubt and I'd like him to have a run with Nicho and Burto and Jarome in the same side', that's where they were with that.”
It's believed Cleary is likely to play, and Fittler laughed off suggestions his halfback could be ruled out, but it may be just 60 minutes prior to Wednesday's 8:05pm (AEST) kick-off where confirmation is received over Cleary's ability to play.