The two clubs have experienced contrasting fortunes since their last meeting in the 2011 Super League Grand Final, with Leeds winning five of six league games so far and picking up the World Club Challenge trophy.
Saints meanwhile, parted company with coach Royce Simmons earlier in the week after they were beaten by Bradford last Saturday, their fourth straight loss and fifth game without a win.
Rush, 36, has been placed in temporary charge alongside Saints legend Keiron Cunningham, and is looking forward to the challenge.
He told the club’s official website: “Of course I want to succeed at this challenge.
“I am a St Helens lad and I never want to see this club not at the forefront of the game, whether that is in developing players or winning trophies. We as a club want to achieve that and I will do everything I can to make that happen.
“Eamonn asked us – myself and Keiron – to step in and do what he thinks is right for the Club at this given moment in time. This is a big club with big expectations and perhaps the players have been feeling that. We want to take a little bit of that away from them and bring a smile back into training. But the players know they have to aim up as well.”
The game kicks off at 6.35pm on Sunday night, and will be televised live on SKY Sports.