The letter was reportedly submitted to the Football League, which oversees clubs outside the Premier League, when Watford were a second-tier club in the Championship.
Watford also announced its own inquiry on Tuesday.
The Daily Telegraph printed a copy of the letter stating that the holding company which owns Watford, Hornets Investment Limited, had sufficient financial resources with HSBC for it to issue a "cash-backed unsecured bank guarantee up to the amount of £7 million" during the 2014-15 season, in which Watford went on to win promotion to the Football League.
An EFL spokesman confirmed that it had started an investigation into "serious allegations" and had contacted the club after receiving information from the newspaper.
"The club is now required to provide a full response to the allegations. Once that response is received, it will be fully considered and appropriate action will be taken under our rules and regulations."
An HSBC spokesman declined to comment when contacted by Reuters.
The EFL spokesman would not comment on assertions in the Telegraph that Watford could face a points deduction or heavy fine if they are found guilty of any offence. The club are currently ninth in the Premier League with 12 points.
The Telegraph said there was nothing to indicate that Gino Pozzo knew anything about the allegedly forged letter despite it allowing him to succeed his father, Giampaolo, as the club's ultimate owner.
Watford FC confirmed its own investigation in a statement on the club's website.
"The club had no prior knowledge of any concerns about the authenticity of the document and Hornets Investments Ltd has invested over £20m into the club since the proof of funds 2014 document.
"The club has instructed independent solicitors to carry out an investigation into relevant matters and provide the EFL with the solicitor’s report early next month. The EFL has indicated it is happy with this course of action."
Giampaolo Pozzo bought Watford in June 2012 from previous owner Laurence Bassini. The Pozzo family have extensive interests in football and also own the Italian club Udinese. They sold the Spanish club Granada to Chinese firm Link International Sports last June.
(Reporting by Neil Robinson; editing by Mark Heinrich)
