Martin missed Saturday night's 51-point loss to Fremantle in Perth due to a back injury and Prestia has been sidelined since injuring his calf against Adelaide on June 6.
Both players will be put through their paces at training over the next few days, with coach Adem Yze hopeful of receiving good news.
"He (Martin) tried to train (last week) and didn't really get through the warm-up, his back was a bit crook," Yze said.
"So it's all going to be around how he feels on Monday and Tuesday, early in the week with those sessions.
"We've got an eight-day break now. So we'll just base it on his body, and if he walks in on Monday or Tuesday and feels like he can train (then he's a good chance).
"And we're getting Dion Prestia (back).
"He was a chance (against Fremantle), so hopefully we'll get him a full week of training and he'll put his hand up for selection."
Yze said forward Tom Lynch (hamstring) was still two weeks away.
Richmond's loss to Fremantle dropped them to last on the ladder with a 2-14 record, putting them 3.8 percentage points behind North Melbourne.
The Tigers take on GWS, Port Adelaide and Collingwood in a tough three-week stretch before coming face-to-face with North Melbourne.
Yze was full of praise for the efforts of skipper Toby Nankervis, who showed plenty of heart against Sean Darcy and Luke Jackson on the way to 26 disposals, 36 hitouts, seven tackles, 11 clearances and one goal.
"We highlighted that post game," Yze said.
"He's our captain for a reason. He puts a team on his shoulders and they follow.
"He's done that for the majority of the year, really.
"He's a guy that really is the most competitive guy in our locker room.
"We couldn't ask any more against two really strong (Fremantle) ruckman.
"We're really proud of the captain's effort."
