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In an interview with AFP, Blatter even called for the opening of an investigation by FIFA's Ethics Commission.
"Mr Infantino is in a situation where he thinks he is untouchable," said Blatter.
Infantino, in charge of world football's governing body since 2016, is the subject of an investigation by the Swiss prosecutor over suspected collusion between him and Swiss Attorney General Michael Lauber, who resigned last month over his handling of a corruption investigation targeting FIFA.
However, Infantino has already insisted he had "nothing to hide".
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In a letter sent to FIFA's 211 members Infantino said there were no "factual grounds for the opening of a criminal investigation".
Blatter was banned for eight years, later reduced to six, for an illicit payment of two million Swiss francs ($2.2 million)made to former UEFA president Michel Platini.
The payment was made in 2011, when Blatter was seeking re-election as president, but was related to work carried out by Platini between 1999 and 2002.
On Thursday, Blatter insisted FIFA's Ethics Commission "should immediately open an investigation and disclose it as they did against me".
However, he then added that the commission "is not independent" because "Infantino has locked the control bodies and this is very worrying".