Quintero, who had been out with a bulging disk in his back, made his Grapefruit League debut on Sunday and caught five innings for the Astros against the Mets. He was 1-for-3 with a line drive single up the middle.
The Royals, looking for a catcher after regular Salvador Perez underwent knee surgery, reportedly had a scout at the game.
Quintero, 32, is in his eighth year with the Astros and is signed to a one-year contract for $1 million. However, the Astros have Jason Castro slated to start, and Quintero is competing with Chris Snyder for the backup job. Snyder has had a good camp and Quintero, because of his back problem, has to play catch-up. The Astros also recently signed catcher Landon Powell.
Quintero has a reputation for calling a good game, and has a strong arm. Last season he played 79 games and batted .240.
Rodriguez, a free agent, previously was reported to have drawn some interest from the Royals.