Aston Villa manager Alex McLeish expected that the Bulgarian midfielder, 32, would spend a couple of days in the capital in the first instance after the diagnosis was made public on Friday and hopes to visit him in hospital this week.
Petrov will initially embark on a course of steroids and tablets that will then prepare him for chemotherapy.
Club captain Petrov addressed the Villa squad in the dressing room prior to Saturday's 4-2 Premier League defeat at home to Chelsea, where he vowed to fight the condition and beat it.
He then stayed on as a spectator at the match 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.
McLeish told Sky Sports News on Sunday night: "I don't think he's down there (in London) long term, only for a couple of days at a time. But we believe he's got the best possible chance of help at the moment, with the specialists he's got now.
"I didn't see him after the game yesterday but he texted me to say it was a great game and he thought we were a bit unlucky.
"He obviously made it a very emotional occasion and the fans were right behind the team and gave us extra power.
"I never realised the Chelsea players wore T-shirts and I thank them very much for that fantastic gesture.
"I watched (Petrov's former club) Celtic play (on Sunday) and they had a smashing tribute in the 19th minute to Stiliyan - he's a massively popular guy.
"I've received numerous emails and texts saying 'pass my best wishes on to him'. Hopefully the support will boost him and give him positivity - I know that can help people in their recovery."
FIFA president Sepp Blatter has become the latest high-profile figure to wish Petrov "strength" as he begins his fight.
Via his Twitter account, football's most powerful man has offered Petrov his encouragement, as Blatter said: "Very sad to hear about Stiliyan Petrov's illness. Wish him strength in his fight to win this battle. Support shown at Villa Park by both sets of fans another sign of all that is good in football. #getwellstan."