Jamar is ahead of schedule in his recovery from a strained PCL and will come straight into the Demons' senior line-up if he gets through training this week.
"I think 'Russian' [Jamar] might be 50-50 for this week," Melbourne coach Dean Bailey said on Tuesday.
"He's been doing some running the past couple of weeks, so he's probably a little bit ahead of schedule, [and] we'd like to think he'd be in consideration for this week."
With back-up ruckman Stefan Martin performing impressively in Jamar's absence, Bailey predicted the returning star could be used in the Demons' forward line, which could combine for only 10 marks inside 50 during the 88-point loss to Collingwood on Monday.
"He's that bigger player in the goal square as a long target for us, which we're missing at the moment," Bailey said.
"He gives us a long target. He's a very good mark."
Colin Garland will also come into the frame for senior selection after playing in the VFL on Saturday.
It was the key defender's first match since injuring his ankle against North Melbourne in round eight.
"He'd only really had two weeks of running, so he needed to play a game," Bailey said.
Bailey said the Demons would need to perform well against Fremantle to atone for Monday's sub-par display against the Magpies.
"Melbourne fans would be very disappointed with the way we played, and so they should be," he said.
"We get judged on how we performed yesterday and it was well below standard, so we've got to make a greater effort next week.
"We've got to be consistent in our efforts, as we've been trying to address on a weekly basis, so next week's performance, actions is what we're after."
Bailey said Sunday's focus would be on improving in contested possession (they were smashed 123-168 by Collingwood) and ball use.
"We've reviewed the game today and we had, I think it might have been 51 or 52 turnovers in the middle of the ground between the arcs, and that's just too many," he said.
"You're leaking goals because of that, and we put our backline under enormous pressure because of the types of turnovers we created through the middle of the ground.
"So we've got to rectify that, and we've got to get our stoppages right, because that's the two areas we really fell down badly in yesterday against an outstanding combination."
Bailey said his club would not take Fremantle lightly despite its long list of injuries, to which David Mundy and Hayden Ballantyne were added after being hurt against Essendon on Sunday.
That list already included star ruckman Aaron Sandilands, plus key players Adam McPhee, Nick Suban and Anthony Morabito.
"I saw them play against Hawthorn at the MCG a couple of weeks ago and they were very, very good," the Melbourne coach said.
"If you talk about the blokes who are out of the team rather than the blokes in the team, then you are not rating them.
"We certainly respect what they do.
"Obviously they're a team that's had injuries during the year, but they've seemed to perform.
"So we'll have our work cut out, but if we can be consistent in our effort then we'll have a great chance of winning the game."
