The 27-year-old successfully fought to be downgraded by the England and Wales Cricket Board's Registration Standing Committee to a List Two player last week to give him the option of being able to join any county.
Sussex are believed to be favourites, but Nottinghamshire are also in the hunt and have held negotiations with Adams.
Dean Jones, the former Australian Test batsman, said yesterday he was prepared to defy a strike, if one is called by the Australian Cricketers' Association, and would even captain the country.
The ACB is believed to be prepared to field a back-up Australian team if the ACA decides to call its members out for either the 4 and 9 December one-day matches against South Africa.
Jones said he would only support strike action if it was solely for better pay and conditions for players in the domestic Sheffield Shield competition.