The Mets' Billy Wagner currently owns baseball's largest contract, earning an average of $10.75 million annually over the course of a four-year deal.
"The ball's in their court," Steinbrenner told The AP. "If they still want to look for more somewhere else, that's up to them."
Rivera's agent, Fernando Cuza, did not respond to telephone messages left by MLB.com.
After finalizing their managerial situation by hiring Joe Girardi to replace Joe Torre and ostensibly cutting ties with All-Star third baseman Alex Rodriguez, the Yankees' main stated priorities for the month included pursuing Rivera and catcher Jorge Posada, both free agents.
Rivera, a lifelong Yankee who has a franchise-record 443 saves and 34 more in the postseason, remains as the mission objective on the club's target list. That follows the Yankees having secured a deal with Posada, hours before he would have become an unrestricted free agent at midnight ET on Tuesday.
Posada agreed to an upgraded version of the three-year, $40 million deal he and Rivera were both presented with, reportedly signing on after the Yankees tacked on a fourth year that brought the total contract to a value of $52.4 million.
Steinbrenner told The AP the Yankees saw good value in the signing.
"He's a catcher, but he can also later on be a DH," Steinbrenner said. "I'm fine with keeping his bat another four years. And as far as the salary is concerned, he was pretty logical. You can't argue with that. He didn't go nuts with what he asked for."
The Yankees likely could have negotiated a contract extension with Rivera -- along with Posada -- in Spring Training, but elected to wait until after the season. Now Rivera is the one forcing the club to wait, at least for another 24 hours.
Rivera was in the Dominican Republic on Monday, where he made a public statement that his first choice would be to return to the Yankees, but he would also entertain the idea of pitching for Torre with the Dodgers.
Aside from their dual pursuits of Posada and Rivera, the Yankees figure to begin testing the trade market as baseball's Winter Meetings approach next month, even as they wait patiently for a final decision from 35-year-old left-hander Andy Pettitte -- mulling retirement at home in the Houston area, even with a standing $16 million contract offer awaiting for 2008.
Steinbrenner told The AP that the Yankees would look into packages for the Marlins' Miguel Cabrera and investigate ace Johan Santana's situation with the Twins, though he cautioned that progress on both fronts "is very preliminary right now."