Martin will not make the trip west to face Fremantle after he was substituted out with a back injury against Carlton on Sunday and was restricted to limited training on Thursday.
His future - whether he continues with Richmond, moves elsewhere or retires when his famous bumper seven-year deal concludes at season's end - is back in focus.
Former mentor Damien Hardwick on Wednesday kept the door open for a reunion with Martin at Gold Coast when he said clubs would be "crazy" not to consider recruiting him.
But Yze laughed off the suggestion from his former Melbourne teammate David Schwarz on SEN radio that Martin had already committed to joining the Suns on a two-year deal at season's end.
"That's all speculation," Yze said on Thursday.
"All I know is walking into the building today, (he's) bubbly, he's enjoying being here.
"As I've said all along, he'll make those decisions in the coming weeks on what he's doing and what his future looks like.
"But right now, he's thinking about getting out there and training and putting his hand up for selection.
"Earlier in the year I did try to push it and say 'let's look at the end of July or the start of August or whatever it is - just so that we can make those decisions' and it's obviously getting closer to that now.
"But we haven't got a timeline on it other than the fact that we just want him happy and healthy while he's here and he can make those decisions."
Richmond are also awaiting a decision on whether vice-captain Liam Baker stays or returns to Western Australia, but aren't putting pressure on him either.
"He's (Martin) been in a really good space for the last six weeks, I reckon," Yze said.
"We had a discussion around that and said, 'let's not think about it until later in the year. And when you come in, let's come in with some energy' - same as the discussion I had with Liam Baker.
"It's too hard to carry that sort of weight when you're trying to work out what you're gonna do and then still perform at a high level.
"So he's in that mode right now and he seems pretty happy."
Yze conceded teams approaching potential recruits in-season reflected a more mature industry and he has no issue with players "ticking all the boxes" when making decisions on their futures.
Martin, who was restricted to light running and walking at training alongside hamstrung spearhead Tom Lynch, was eventually ruled out of the Freo clash.
"One, we want to make sure his back is okay, and then we'll make a decision on his full body and whether the six-day break and the travel is going to be a bit too much," said Yze, before the late afternoon call.
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