The striker is currently out of favour at Liverpool.
Liverpool's Daniel Sturridge arrives before the match
The striker has found himself out of the first team ever since Jurgen Klopp arrived at the club last October.
He has once again been on the bench this season, playing a peripheral role as Roberto Firmino has shined in the centre forward position.
As a result, rumours about his future have steadily gathered pace, with reports he could even be set to depart in the January transfer window.
Rush believes his old team will need the England man, though, and warns him that sulking will not get him anywhere.
“We’re going to need Daniel Sturridge. He’s got to be patient and his time will come” said Rush, speaking to 888Sport.
“He’s the best finisher at the club and he’s absolutely superb but he needs to get his head down and get on with it. Sulking doesn’t help anyone."
Liverpool's Daniel Sturridge warms up during the game
It will certainly be interesting to see what happens with Daniel Sturridge in the coming months.
There is no denying he will be useful in Liverpool’s bid for the title this season, especially if the Reds pick up any injuries to men such as Roberto Firmino.
However, if a big bid were to come in for his services, which could happen given the teams that are in need of a player of his quality, it is easy to see why the Reds would be tempted to sell.
It is a dilemma for Jurgen Klopp and it will be fascinating to see what decision the German makes.
Liverpool manager Juergen Klopp with Daniel Sturridge as he prepares to come on