Billiat is free to sign a pre-contract with any team as his deal with Sundowns is due to expire in June.
This website has gathered that Pirates have submitted a new offer to the Zimbabwean's representative after their initial offering was turned down.
"Pirates have been talking to the player's representative," says a source.
"The first offer was rejected. They have made another offer."
Billiat is believed to be earning close to R160 000 a month at Chloorkop before deductions, with the club prepared to increase his salary by R40 000 to keep him.
Azerbaijan champions FK Qarabag and Kaizer Chiefs have also been linked with a move for the 27-year-old.