Draper was substituted out of Essendon's win against Carlton in round 13, with coach Brad Scott indicating he would prefer to get the dynamic 24-year-old fully fit rather than play him hampered.
Parish will return after missing five games with a calf injury. He trained well on Wednesday but teammate Draper wasn't on the track.
Losing Draper would be a hefty blow to Essendon's hopes against the Dockers, who should regain big man Sean Darcy (hamstring) to partner Luke Jackson at Optus Stadium on Saturday.
"I'm not as positive on Drapes as I am Darcy (Parish)," Scott told reporters.
"He has been getting out there and playing but we're just concerned that he's a really dynamic player.
"We want him at his best and he has been struggling with a niggle.
"Unless he presents really well and proves he's 100 per cent right to go, then we'll probably err on the side of getting him right.
"We'd love to have him out there but again, he's just a really important player for us and we've been really consistent throughout this year that we want players out there at their best."
Scott said Draper's condition had improved after the bye but the injury could take a couple more weeks to clear up.
"This stage of the season, we're better off getting it right, as long as that takes. It's really difficult to give you a time frame," he said.
"It could be next week, could be longer. The only reason we're vague is because we don't know ourselves."
Young tall Nick Bryan could be called up to partner Andrew Phillips, with the Bombers generally preferring two rucks.
"Fremantle are a very good clearance side," Scott said.
"When they play their best they're pretty dominant in that part of the game. So that usually starts with the ruck options.
Parish averaged 33.5 disposals and 8.5 clearances before his injury and should slot back into a midfield that has stood up in his absence.
"He should be (back). That's been our loose plan all along, post-bye, and he's done a power of work. It's been a pretty conservative rehab," Scott said.
"He's trained really well through the bye week and he'll train again today and we expect to select him tomorrow."
Dylan Shiel (foot) appears unlikely to return, with Scott keen for the dashing midfielder to regain full fitness before throwing him back into the fray.
