Ajax Cape Town and a Danish side yet to be named have also joined the race to sign the Zimbabwe youth international, whose move to France has been put on hold.
"Chiefs have come with an offer as well as Ajax and a Danish top-flight team. So, the player's agents are just assessing their options and will make the decision this weekend. Chiefs looks to be the most likely destination," a source privy to the negotiations reveals.
Rusike was initially tipped for a move to Europe, but the trials have been put on hold pending discussions with local sides.
The 21-year-old starred for Cosmos last season, although he could not save them from relegation.
The former University of Pretoria forward has previously secured a trial at Bolton, then in the English Premiership, but an injury hindered the move.
Rusike sustained an ankle injury when playing for the Zimbabwe national Under-23 team last year just before he was set to leave for England.