McGovern has been sidelined since tearing his hamstring in the round-three western derby loss to Fremantle.
The four-time All-Australian is back in full training and barring any late setbacks is on track to return in Saturday's clash with Sydney at the SCG.
Fellow defenders Tom Barrass (hip), Liam Duggan (toe) and Shannon Hurn (hamstring) could also join McGovern in the side in what would be a huge boost on the back of the embarrassing 122-point loss to Adelaide before the bye.
That defeat - the biggest in coach Adam Simpson's 10-year reign - was West Coast's 11th straight loss.
It left the Eagles on the bottom of the ladder with a 1-12 record and a woeful percentage of 51.4.
But with McGovern, Barrass, Hurn and Duggan all set to return either this week or next - and with Elliot Yeo, Luke Shuey and Jack Darling having made recent comebacks - West Coast will finally be able to field a competitive side.
Young midfielder Elijah Hewett (concussion) is another player who is available for selection this week, while Jamie Cripps (ankle) and Tom Cole (ankle) are set to return in the next two to three weeks.
"If there was a game last week, I reckon he (McGovern) would have played a bit of WAFL," Simpson told the club's website.
"The guys returning are quality players who we have missed - McGovern, Barrass, Duggan, Hurn, Cripps, Cole.
"We're hoping to get them back in the next couple of weeks.
"The standard has lifted at training, that's for sure. They're quality players and really hard to replace."
With a host of West Coast stars on the verge of returning, there's renewed hope the Eagles can avoid the wooden spoon.
North Melbourne currently sit a win and 18.2 per cent ahead of West Coast, with the two struggling sides set to clash in Perth in round 20.
Eagles forward Jake Waterman, who spent eight days in hospital with a stomach infection, is likely to miss at least one or two more weeks, while Liam Ryan (hamstring) faces a fight to play again this year.
Ruckman Nic Naitanui has already been ruled out for the season after undergoing surgery on his troublesome Achilles.
Simpson confirmed mid-season draftee Ryan Maric, who booted two goals against Adelaide, would keep his spot in the side against the Swans.
Defender Luke Foley is set to miss the clash with Sydney after injuring his hamstring against Adelaide.
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