Rangers met with OF Cody Ross and are checking into Michael Bourn

The Rangers, Red Sox and Mariners have shown interest in Bourn. (US Presswire)

The Rangers, still looking to upgrade their offense after agreeing to terms with veteran catcher A.J. Pierzynski, are staying in touch with free-agent outfielder Cody Ross after having a meeting with him. But Texas is also starting to look into free-agent outfielder Michael Bourn.

The Rangers appear to be looking into several ways to improve their offense and pitching staff after losing superstar Josh Hamilton to the rival Angels and failing to land a trio of big pieces -- Zack Greinke, Justin Upton and James Shields. The deal with Pierzynski, for $7.5 million for 2013, may just be the start.

Ross is said to have received a lot of interest, with the Phillies, Mariners, Red Sox and Indians hovering among the other possibilities, following a superb season in an otherwise dreary Boston year. Ross dined with Rangers decision-makers within the past few days.

A possible run at Bourn seems to be more in the infancy stages, with Texas people asking around about Bourn, who has an impeccable reputation but mostly a mystery market thus far. The Mariners are known to have interest in Bourn, while the Red Sox are a team that's checked in as well, though their interest may depend on a trade or injury.

The Braves still seek a leadoff hitter for left field, but Bourn's big value is as a center fielder, where zone ratings suggest he's saved a league-best 81 runs over the past four years. The Dodgers are thought to like Bourn, but with Carl Crawford expected back at the start of the season and the Dodgers suggesting no expectation to trade Andre Ethier (despite reports, they are known to have told at least the Red Sox that Ethier is "not available"), it doesn't appear there's room now for Bourn in LA.

The Rangers have any number of ways they can go with their offense. While they have a very talented center-field prospect, Leonys Martin, it's uncertain whether he's ready. Their corner outfielders are Nelson Cruz and David Murphy as things stand.

The Ranger also are looking to add a starting pitcher. They made a bid for Edwin Jackson but weren't willing to offer him four years before he agreed to a deal with the Cubs for $52 million over four.

The Rangers have lost Mike Napoli, Michael Young, Scott Feldman and Koji Uehara, and only gained Pierzynski so far, so there's plenty of room for acquisitions.