The 22-year-old strained the medial ligament in his right knee late in the first quarter of Friday night’s 37-point preliminary final win over Geelong.
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Aliir succumbed to the game-ending injury in a marking contest against Cat Lincoln McCarthy, but was walking unaided post-match and at the airport on Saturday.
Swans head of football Tom Harley said Aliir would be given every opportunity to prove his fitness.
“The scans have revealed Aliir has suffered a low-grade medial strain,” Harley told sydneyswans.com.au on Sunday.
“We will continue to monitor Aliir and assess him as the week progresses. He remains a chance to play.”