"I admire the work of Mauricio and Jurgen, both deserve to achieve something big and there is nothing greater than holding the Champions League".
"Manchester City FC is fully cooperating in good faith with the CFCB IC's ongoing investigation", the statement said.
In a fresh statement issued on Tuesday, the club further maintained it meant to cooperate fully with UEFA's investigation.
Manchester City have not commented on the video.
Uefa opened a formal investigation into City in March after a report in German magazine Der Spiegel, based on documents obtained by the Football Leaks website, claimed that City had been disguising huge investment from its owner, Sheikh Mansour bin Zayed al-Nahyan, as sponsorship deals through various UAE-based companies.
UEFA are looking to slap a 1 year ban on Manchester City, and will be advocating for that punishment in the coming month or so.
City, who were fined 60 million euros (S$92.2m) and subjected to squad, wage and spending caps in a 2014 settlement agreed with Uefa following a previous breach of the rules.
Sheikh Mansour bin Zayed al-Nahyan, the billionaire businessman and member of the Abu Dhabi royal family, bought Manchester City in 2008.
City issued a strongly-worded statement on Tuesday with concerns that someone said to be close to the investigation, conducted by the investigatory committee (IC) of the Club Financial Control Body (CFCB), has released information.
It is unclear which players and staff - if any - are joining in the song, which recalls Liverpool's defeat in last year's Champions League final in Kiev.
Guardiola's City retained the Premier League title on Sunday, beating Klopp's Liverpool by a single point at the end of a thrilling title race.
City will become the first team in history to win a domestic treble when they beat Watford in Saturday's FA Cup final and I see them repeating this level success time and again over the next few years.