Finn injured his left knee while batting at training, while Ali is troubled by a side strain and played no part in Thursday's session.
Both players are to undergo precautionary scans on Friday. England begin their tour with a two-day game against a West Australian XI from Saturday.
It represents the first injury scare for the tourists, who play three warm-up games before facing Steve Smith's Australia in the first Test in Brisbane on November 23.
Finn, who was a late call-up for suspended all-rounder Ben Stokes, was struck on the knee while batting in the WACA Ground nets.
The bowler, who has played 36 Tests, starts the tour behind Jake Ball and Craig Overton in the running to replace Stokes in the final XI.
But Ali, who has played 44 Tests, is a key player in a touring party that is lacking many hardened veterans.
With Western Australia's best players on Sheffield Shield duties, England will face a second-string WA XI squad in the two-day match starting at the WACA Ground on Saturday.
Only two players in the squad, captain Nathan Coulter-Nile and all-rounder Will Bosisto, have Shield experience.
First Published: November 2, 2017, 2:37 PM IST