With the Eels having around $500,000 to spend, their hopes of snaring Cooper hinge on whether the NRL is prepared to bankroll the biggest Wallaby defection since rugby turned professional in 1996.
Alexander said the NRL would be foolish to ignore the public relations opportunities in poaching Cooper after seeing big-name stars Craig Gower, Karmichael Hunt, Sonny Bill Williams and Israel Folau lost to rugby and AFL in recent seasons.
"It is time for the NRL to do something. Let's get Quade Cooper," Alexander said. "Why not do it? The other codes have done it to us, why shouldn't we do it?
"I know it wouldn't be a popular decision [for the NRL to subsidise Cooper's Eels deal], but if a guy like Quade Cooper is interested in league, we shouldn't be closing the door on him. The AFL stepped in to help get Israel Folau, the ARU has stepped up previously to top-up several league guys' contracts like Mat Rogers and Wendell Sailor.
"If I was David Gallop [NRL boss], I'd be saying here's some money, pick which club you want to play with and we'll give you a top-up. I know NRL clubs will jump up and down, but Quade Cooper would be a massive coup for the game.