The Australian posted a training photo on social media, tagging the Brazilian and hashtagging the event number.
A few days earlier, Costa informed his fans that he intends to take part in the UFC 297 tournament, which will take place on January 20 in Toronto.
Robert Whittaker, 32, was defeated in a challenger fight in July, losing to Dricus Du Plessis by technical knockout in the second round.
Paulo Costa, 32, last fought last August, defeating former division champion Luke Rockhold by unanimous decision over three rounds.
Whittaker and Costa were scheduled to meet at UFC 284 in Perth last year, but the bout was canceled due to protracted negotiations over the Brazilian’s new contract.
Robert Whittaker and Paulo Costa are currently ranked third and sixth in the UFC’s middleweight division rankings, respectively.