"It's really early days and [Ogilvy and I] are going to sit down in a couple of weeks at the Australian PGA," said Allenby, who spoke at a public memorial service for Lyle in September.
"We'd like a tournament in Melbourne and to get a Jarrod Lyle Invitational going. That's something that [Ogilvy] and I have spoken about.
"We'll get some ideas down and obviously we need the Victorian Government to support it and we'll look after the players. The tournament would all be about Jarrod and his legacy. Millions and millions and millions of people followed him over the years and his true fight.
"I think if you've got a heart you would come and play [in the tournament]."
Melbourne will host next week's USPGA Tour-sanctioned US$7 million World Cup of Golf as well as the 2019 Presidents Cup, featuring sides led by Tiger Woods (United States) and Ernie Els (Internationals).
But the city has been without a regular tournament on the Australasian tour since the Australian Masters ended in 2015.
"[This tournament will] not [be] for one year but for a long time," Allenby said.
"Melbourne has the best golf courses in Australia and we need to have a legit year-in-year-out tournament. Whether it's at Peninsula Golf Club or Victoria or Royal Melbourne or Metro or Kingston Heath, we'd love to create something. Something like the Masters once had.
"I think there's a lot of companies out there that would love to be a part of it and we'd love to be the first tournament on tour that generates money for charity. Obviously Challenge would be one of those beneficiaries and that's because it was Jarrod's legacy.
"Why not keep that going and be one of the first events on the Australian tour to give back to charity and help kids with cancer because that's what Jarrod was all about? His attitude on the golf course was the same he had off the course. I just hope people don't forget about him too quick."