The Angels have only one free agent, pitcher Jason Vargas, and they have until 2 p.m. Monday to decide whether to extend a one-year, $14.1-million qualifying offer to the left-hander who went 9-8 with a 4.02 earned-run average in 24 starts during an injury-plagued 2013 season.

The Angels are not expected to make that offer because it would push them up against the $189-million luxury tax threshold for 2014, but that wouldn’t preclude them from pursuing a multiyear deal with Vargas, who has expressed a desire to remain in Anaheim.

If they made a qualifying offer to Vargas, who would probably decline it, the Angels would be entitled to draft-pick compensation if Vargas signs elsewhere.

Vargas, who has a 51-58 career record and 4.30 ERA in 174 games over eight seasons, missed almost two months from mid-June to mid-August because of surgery to remove a blood clot in his left armpit.

The Angels made two huge splashes in free agency the previous two winters, signing first baseman Albert Pujols to a 10-year, $240-million deal before 2012 and outfielder Josh Hamilton to a five-year, $125-million deal before 2013.

But payroll concerns — the Angels have $126.5 million committed to 10 players, including New York Yankees outfielder Vernon Wells for 2014 and would need about $20.5 million to retain their eight arbitration-eligible players — are expected to keep the Angels out of the high-end free-agent market this winter.