"I think we might have one or two [players entering protocols] floating around," Simpson told Seven News on Monday night.
Simpson added: "We're just working through it today. You'll find out as soon as we let you."
There is no indication as to who those players might be, either, as the only noticeable absence from Eagles training on Monday was midfielder Elliot Yeo, who entered concussion protocols this week after suffering a head knock during last Saturday's loss to Port Adelaide.
However, in more positive injury news, star intercept defender McGovern and ball-magnet Gaff are likely to return for this Friday night's clash with Richmond at Optus Stadium.
"Hopefully 'Gov' is available this week, just needs to tick all the boxes, same as Andrew," Simpson said.
"We won't take any risks on those players.
"'Gaffy' has been a few weeks now, he missed a week with the same injury, came back and missed a couple of weeks. We'll have that discussion later in the week."
The Eagles, who have already used 41 players so far this season, may be set to unleash another debutant this week.
Mature-age midfielder Greg Clark, whose start to the season has been injury-interrupted, was influential in the WAFL last weekend and finds himself in the selection frame this week.
"He was pretty good on the weekend," Simpson said of the 24-year-old. "Unfortunately he had a good pre-season until he popped his shoulder, so he missed a good six or seven weeks.
"He falls under the same category as a lot of our players who are returning to play, I think he's played two games now of WAFL footy.
Week one done for Brady Hough, Jack Williams, Greg Clark & Rhett Bazzo! pic.twitter.com/Znthx9Q2Sj
— West Coast Eagles (@WestCoastEagles) December 3, 2021
"He looks like he's running on top of the ground and he looks pretty good so he's definitely in the mix this week."
West Coast will be looking to earn its second win of the season when they face the 2-4 Tigers.