Draper is an unrestricted free agent this year, with Adelaide's long-time interest in luring the 26-year-old cult figure away from the Bombers well known.
But after a strong start to the season, Draper went down with the devastating achilles injury in Essendon's two-point win over West Coast on Friday night.
Draper will undergo surgery to repair the damage in the coming days and is set to be sidelined for an extended period.
"We're absolutely devastated for 'Drapes', who's had a terrific start to the year," Essendon football manager Daniel McPherson said.
"He's worked so hard over the course of the pre-season and had started the season really strongly.
"Sam's obviously an important player for us, but he's also such a beloved member of this group by players, staff and fans alike.
"We'll support him through his rehab."
Draper's setback, in addition to Nick Bryan's season-ending knee injury, means Essendon will turn to 36-year-old veteran Todd Goldstein to lead the ruck in the Anzac Day blockbuster against Collingwood.
Adelaide, meanwhile, are breathing a sigh of relief after star forward Darcy Fogarty avoided a major shoulder injury.
Fogarty had been forced out of the Crows' 18-point win over GWS in the third quarter on Saturday after a bump from Giants defender Harry Himmelberg.
He returned to the game, before the left shoulder complaint proved too much, finishing with only eight touches.
Scans later confirmed Fogarty has sprained his sternoclavicular joint - the ligaments where the collarbone meets the sternum.
Fogarty has led the fifth-placed Crows in attack this season, equal will Riley Thilthorpe with 16 goals each.
The key forward has not yet been ruled out of Adelaide's clash with Fremantle on Anzac Day.
"We will need to let it settle for a couple of days, so he will be on light duties, but in short there is no major structural damage, which is pleasing," Adelaide high-performance boss Darren Burgess said.
"It's too early to rule him out of the trip to Perth, but his availability will obviously depend on how he responds during the week."