Daryl Katz, owner of the Rexall Pharmacy chain, is believed to have put up more than $170 million. Previous offers of $150 million and $145 million were made to the board of directors but were rejected.
This time, however, Katz has reportedly gone directly to shareholders with his bid.
All Katz needs is two-thirds of the votes for the sale to go through.
The Oilers are currently owned by 37 investors who bought the NHL team in 1998.
Katz is listed by Forbes magazine as the 486th richest man on the planet. Last year his net worth totalled $1.6 billion.
When Katz made his last offer in May, investors group chairman Cal Nichols insisted a sizable majority of the owners did not want to sell the team.
"There was more an appetite to stay," Nichols said at the time.
"This group has endured a lot of pain and agony and expense. It was more like, 'Surrender now?' There's brand attachment with a lot of the individual businesses and that's important here."