The Hoops chairman, who has 285,802 Twitter followers, is a regular user of the social network site and has been seen to post updates during QPR matches.
Redknapp has admitted it would be a "massive loss" for the club if Fernandes left and has encouraged him to close his Twitter account to prevent similar incidents happening in the future.
"The only advice I'd give Tony is get off Twitter," he added. "If you don't want to know what people are saying, don't be on Twitter."
Rangers are currently bottom of the Premier League.