Governing body SANZAAR said last Sunday the Super Rugby competition would be cut from 18 teams to 15 from next year with South Africa to lose two sides and Australia one.
The Australian Rugby Union (ARU) said on Monday either the Perth-based Western Force or Melbourne Rebels would be axed, but then delayed the timing of that decision after the Force instigated legal action.
The Australian players' union have vented their anger at the cuts, while several players have expressed concerns about their playing futures.
Cheika told local media that the uncertainty could impact performances on the field and said he would do all he could to ensure axed players were signed by Australia's four other Super Rugby franchises.
"No one wants to play in the unknown," Cheika said in comments published by Australian Associated Press. "The idea is that we try to make sure that everyone comes out in the best situation they can.
"That's important to me because, even at the national team level, apart from the players, that doubt can have a knock-on effect into performances.
"When I say performances, I don't think it has an effect on tackling people or catching balls or catching kicks, more the mental side."
Cheika added that through natural attrition -- players leaving for overseas contracts, retiring or simply being cut -- many of those left out of a job when their team is cut should be able to be accommodated by the remaining sides.
Any promising player who missed out on a contract, but who he felt had potential to make the Wallabies, would be signed to an ARU contract, Cheika said.
"We're losing too many players overseas," Cheika said. "Especially the younger market, which we're targeting now, because we want the younger players to come through.
"We understand that we don't have as many resources (as Europe and Japan) and we've got to make sure our good players make it (to the top level).
"That will help our market place all round because then, when our top-end players get huge offers from overseas and they might start considering them, we've got young players who might come and fill those voids."
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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