The Australian limited-overs player will bat if required as the Warriors chase 256 to beat the Tigers on Saturday's final day in what would be their tenth most-successful fourth-innings run-chase at home.
At stumps on day three on Friday, WA were 2-27 with Marcus North unbeaten on 12 and Marcus Harris one not out.
Andrew Fekete did the damage for the Tigers with the ball, claiming the wickets of opener Cameron Bancroft for 10 and nightwatchman Michael Beer for four, both lbw.
Coulter-Nile, taken by the Delhi Daredevils in the IPL player auction for $708,000, was unable to take his place on the field for the Warriors on day three and will require a scan to determine how much damage has been done.
Coulter-Nile has some time to prove his fitness, with the Daredevils kicking off the tournament on April 3 against Kolkata.
Experienced Tigers batsman George Bailey and Ed Cowan took advantage of his absence. The pair's patient third-wicket partnership of 136 runs was the basis of Tasmania's total of 286 runs after they conceded a 31-run deficit on the first-innings.
Cowan was the first Tasmanian batsman to fall on Friday, caught at backward point off the bowling of spinner Marcus North for 59 from 178 balls.
He departed midway through the second session and was quickly followed by Bailey (83) three balls later, who was caught behind from the bowling of Mitch Marsh.
Marsh finished with the best figures of the Warriors bowlers, taking 4-35 from 13 overs.
He had Tim Paine caught at first slip the over after snaring Bailey and when Ryan Duffield took the first of his three wickets four overs later, Tim Paine for just four, the Tigers had slumped from 2-200 to 6-217 in just seven overs.
Marsh said the WA bowlers fought back well after the loss of their strike bowler.
"We're definitely happy chasing that after they were 2-200," Marsh said.
"Down a bowler, we fought back really well as a bowling unit, so to be chasing 250 on that wicket; the wicket is beautiful, so we have given ourselves every chance.
"If you go searching (on this wicket) you get punished. We just knew if we stuck in there we'd get the break through and we bowled really well towards the end of the day and we got our rewards."
Some big hitting by Ben Hilfenhaus (29) and Sam Rainbird (32) late in the innings got the Tigers to a competitive total.