Draper earned the ire of both Bulldogs and Bombers officials after weighing in on Beveridge's coaching tenure.
On the 200 Plus podcast, Draper - in a segment where he was imitating a journalist - said he had a "big call" about the Bulldogs.
"If Bevo is still there, there will be some players requesting trades," the 25-year-old said.
In a surprise turn of events on Thursday evening, the Bombers revealed Draper will miss Saturday night's clash with West Coast in Perth due to knee soreness.
Beveridge weighed in on Draper's comments, even though he had planned not to say anything about it.
"It was bizarre to me," Beveridge said earlier on Thursday.
"... the people who became aware, who are close to him, the football club, (were) extremely alarmed and reached out to me to express their apologies.
"My number one concern is our players and taking care of them and (making them feel) supported.
"When something like that happens in regards to me I can deal with it, but it's unusual."
Western Bulldogs coach Luke Beveridge talks tactics during a break against the Dockers. (Richard Wainwright/AAP PHOTOS)
Beveridge was asked how he would feel if one of his Bulldogs players made similar comments about an opposing coach.
"This is normally one where I'm sure that he (Draper) has had a think about it and maybe he wouldn't do it again, I'm not sure," he said.
Injured midfielder Bailey Smith is one player heavily linked to moving to another club.
Smith, who will miss the entire 2024 campaign and is off-contract at season's end, has been completing some of his rehabilitation away from Whitten Oval.
"The good thing is Bailey is back running on the grass now … feeling pretty good about himself ... and that will help with his peace of mind and feeling really positive about his return," Beveridge said.
"His contact hours have gone right up now that he's back doing a lot more."
The coach said forward Jamarra Ugle-Hagan "should" be right to face Hawthorn at Marvel Stadium after he missed the past two games due to personal reasons.
"He wasn't too far away from being able to play last week, but on such an interrupted preparation, it's a better idea for him to have another week off and get some some momentum," Beveridge said.
Star midfielder Tom Liberatore will almost certainly be back to face the Hawks after missing last week's defeat to Fremantle due to illness passed on by his son.
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