The Toffees are just a single point above the drop zone at present and are facing the prospect of suffering relegation from the top flight for the first time since the 1950/51 season.
While Everton are toiling down at the bottom half of the table, neighbours Liverpool are chasing the league title and many among the Reds faithful are keen to see their eternal rivals suffer the humiliation of losing their top flight status.
However, Reds legend Rush has insisted that Everton slipping down to the Championship would be a real shame for the city of Liverpool, as the Merseyside derby would not be on the Premier League calendar for at least a season.
Rush stressed that the derby against Everton is one of the special games Liverpool fans look forward to at the start of every league campaign and he feels losing such a clash steeped in history would be a sad affair.
“I’ve heard a few people say they’d love to see Everton go down but I don’t, personally”, Rush wrote in his Gambling.com column.
“For the city of Liverpool, it would be a real shame to lose the Merseyside derby even if it was only for one Premier League season.
“I would be sad if they got relegated and I’m sure there’s a lot of other Liverpool fans out there who’d feel the same, because it would take something special away from next season.
“Everyone looks for the derby dates once the new season fixtures are announced, imagine the fans not being able to do that?”
Anfield will host the second Merseyside derby of this season on Sunday, which will be a must win game for both Liverpool and Everton; for the Reds to keep their title hopes alive and for the Toffees to take one more step towards safety.