The former World Player of the Year is unattached after leaving Sao Paulo, but is not wanted by the current Belgian champions despite being available on a free transferhere.
Genk have turned down the opportunity to sign former Barcelona and AC Milan attacker Rivaldo, according to Sportwereld.
The former Brazil international is currently a free agent after parting company with Sao Paulo, and has vowed to play on until the end of 2012.
With the 1999 Fifa World Player of the Year available immediately at no cost, the Belgian newspaper indicates that the South American's agent has been in touch with the current Pro League champions.
Despite this, Mario Been's side are believed to have opted not to add the 39-year-old to their squad.
Rivaldo shot to fame playing in Europe at the Camp Nou and Giuseppe Meazza, and will now need to continue his search for a new club before he finishes his playing career.
Genk are currently second in their domestic league, one point behind leaders Anderlecht after 19 games.