Would the Padres trade right-hander Mat Latos?

Better question: Why wouldn’t they?

True, Latos is still affordable; he isn’t eligible for salary arbitration until 2013. But the Padres, a low-revenue team, are trying to improve through trades, not free agency. And two of their most available players, second baseman Orlando Hudson and shortstop Jason Bartlett, are drawing little interest.

Third baseman Chase Headley, entering his second year of arbitration, is the Padres player most in demand and most likely to be moved, sources say. A number of teams are seeking help at third, and third baseman Jedd Gyorko, one of the Padres’ best prospects, finished last season at Double A.

The Padres, though, are not in position to rule out anything. New general manager Josh Byrnes is willing to talk about every player on his roster, sources say. He is not shopping Latos, sources say, but rival clubs are inquiring.

The discussions won’t necessarily lead to a deal; a number of other starting pitchers are available, and Latos’ ERA jumped from 2.92 in 2010 to 3.47 in ’11. The Padres might prefer to wait, figuring his value will be even higher if he returns to his previous form.

Then again, the Padres are not one or two players away from contending. Their organizational depth is improving. If they could land a strong multi-player package for Headley and another for Latos, their pool of young talent would be that much greater.

It’s not likely the Padres will trade Latos, but you never know where discussions might lead. For now, only one thing seems certain: The Pads will be active, and soon.

-Ken Rosenthal