Chagaev, who is under investigation in Switzerland for falsification of documents and money laundering, is believed to only have a basic visa that must be renewed every six months, and only after leaving the country.
Le Matin reports that Chagaev was unable to produce a valid visa when police visited him at his office in Geneva.
"He is an illegal immigrant that could be thrown out of the country at any time, just like any other foreigner who is on Swiss soil illegally," claims the paper.
Le Matin also reports that Chagaev gave a Bank of America headed letter to the Swiss Football League signed by a so-called Tomas Milller -- with three 'l's -- a mistake that they believe will not have gone unnoticed by investigators.
The letter is in the hands of police, along with another letter, pertaining to be from the Bank of America, which attests that Chagaev has an account containing $35 million.
In the last 10 days, police have issued warrants to search Chagaev's offices in Geneva, his home near Lausanne and Neuchatel Xamax's club offices.