Villa owner Randy Lerner, chief executive Paul Faulkner and McLeish visited Petrov in the London hospital where he will be undergoing treatment after news of his condition was announced on Friday.
The Scot said: "Stan is determined to meet it head on, as we'd expect from him. He's talking really positively and couldn't wait to get started to try to beat off this illness that he has."
He continued: "The support he's had from Villa, the fantastic show of strength from Celtic, the support from Chelsea on Saturday, and the response from the football family has made him delighted and proud.
"Stan himself is in amazing spirits, absolutely fantastic spirits. God knows what the lad is thinking in his head, but he is the captain of Aston Villa. He's shown the commitment on the pitch as a pure leader, and he wants to lead himself through this particularly tough thing."
The wave of goodwill for Petrov was notable during Villa's 4-2 Barclays Premier League home defeat to Chelsea when players from both clubs wore T-shirts showing their support during the warm-up.
The 32-year-old addressed the Villa squad in the dressing room prior to the match. He then stayed on as a spectator with his family, and stood to acknowledge an ovation from both sets of supporters in the 19th minute - timed to match the player's squad number.
His former club Celtic embarked on a similar tribute during their 2-0 defeat of St Johnstone on Sunday.
McLeish insisted it was too early to think about the long-term effects of Petrov's illness, and asked for his privacy to be respected in the months ahead.
The Villa boss said. "He faces a battle and he will stand up to that battle. He's talking about coming to training because he feels as if he could train. That's the kind of spirit he's in. Everybody is here to support him. We thought it was appropriate that we should be there with him on his first day of recovery."