Sheed has been struck down with a hot spot in his foot and, although he'll avoid surgery, the Eagles are unlikely to play him again this year.
"We will lose Dom, possibly for the season," Simpson told reporters on Thursday.
"He's got a hot spot there. Whether he gets back this year or not, he's trying really hard to play and support.
"It won't be surgery, just time off legs. Whether it's two weeks, one week, six weeks - we'll work through how that pulls up in the next 10 days.
"But there's four weeks left, he's coming off (almost) no games last year (with a) syndesmosis.
"I'm not surprised there's been issues here and there. We need to look after him."
Sheed, who kicked the winning goal in the 2018 grand final, has played 15 games this season, and his injury is another blow to the already-depleted Eagles.
Hawthorn are reportedly keen on luring Ryan their way, but Simpson is confident the 26-year-old will stay.
"He's a contracted player. He's entrenched in WA with his family," Simpson said.
"He's had a lot of support with us. I would have thought Liam is going nowhere."
Defender Jeremy McGovern (concussion) is set to return for Saturday's clash with Essendon at Marvel Stadium, while last week's sub Elliot Yeo will be handed a start.
Retiring defender Shannon Hurn will miss due to soreness.
West Coast ended their club-record 16-match losing streak last week with a thrilling five-point win over North Melbourne at Optus Stadium.
The result means last-placed West Coast are now just percentage adrift of 17th-placed North Melbourne.
One more win for the season could be enough for West Coast to avoid the wooden spoon, but it would also mean missing out on the prized No.1 draft pick and the chance to snare gun midfielder Harley Reid.
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