Photos on social media showed the bedsheet, upon which was written the message: "we know where you live don't sign".
It was placed over a wall on a driveway in Caldy, Wirral.
Merseyside Police confirmed officers were investigating the banner after it was reported at 7am on Monday.
Former Liverpool manager Benitez is reported to be in talks to replace Carlo Ancelotti at arch rivals Everton.
Detective Inspector Darren Taylor said: "This message has understandably caused some distress and worry for residents in the area.
"Due to the football language used, we suspect that it was aimed at Rafa Benitez - but whoever placed the message left it outside the wrong house.
"If anyone has information about who produced the banner or helped to put it up, please let us know as soon as possible."