The 25-year-old was absent from the Eagles' open training session on Wednesday morning as he recovers from a stress reaction in his shin.
Wellingham has been in rehab for a couple of weeks and is expected to return to full training shortly.
The Collingwood premiership player was plagued by injury in his first season at West Coast.
He suffered a nasty ankle injury during the 2013 pre-season after falling off a trampoline.
He missed the first five matches of the year before injuring his other ankle in round eight against North Melbourne and missing a further seven matches.
Defender Jacob Brennan is also battling a similar stress reaction to Wellingham and was on light duties at training on Wednesday.
Beau Waters is still recovering from complications with his shoulder surgery and was consigned to running with new recruit Malcolm Karpany.
The Eagles trained strongly in the morning heat at Patersons Stadium doing a number of full ground skills drills.
Nic Naitanui participated fully in the session, as did youngster Jeremy McGovern who has worked his way back to full fitness after being forced to train away from the main group at the start of the pre-season.
Former Hawthorn midfielder and free agency recruit Xavier Ellis was impressive during the skills session and should push strongly for selection in round one.
