By Bruce Levine–

GLENDALE, Ariz. (CBS) — Please don’t think the Chicago White Sox are finished tweaking their 25-man roster for 2016.

General manager Rick Hahn and the front office have been working hard on adding a quality outfield bat since early November. They continue to burn the midnight oil to add a left-handed bat to the mix.

Free agent outfielder Dexter Fowler, a switch-hitter, is still a possibility for the White Sox. He’s been hearing from three teams — the White Sox, Rangers and Orioles. At last look, opening day is still 44 days away. The idea that someone will blink and give Fowler a three-year deal is certainly possible. Will it be the White Sox on that sort of deal? Probably not.

Fowler’s a good player whom many believe is a late bloomer. He played in the most games of his career with the Cubs in 2015 and scored 103 runs, one of the metrics that’s intriguing to the clubs that are still considering adding him. Hitting at or near the top of the White Sox order with a career .363 on-base percentage is an even more intoxicating number to munch on.

Other variables surrounding Fowler trouble the numbers people. A career-high in strikeouts and a .233 batting average in the first half of last season — he finished at .250 for the year — are factors to consider. Fowler hadn’t averaged more than 130 games played per season until 2015. The defensive metrics also tell you he’s at best average in the field, so the jury’s still out on that one.

The Cubs will tell you that without Fowler putting up his numbers in the second half of 2015, they would have had trouble making the playoffs.

Hahn and company would lose the 28th pick in the draft by signing Fowler. That selection comes from the Giants’ signing of right-hander Jeff Samardzija. The slot money is maxed out at $2 million, which is dirt cheap for a high pick.

“The draft pick has real value,” Hahn said Friday. “Don’t get me wrong. That pick has real value. Having three picks in the top 48 would be a nice thing for the organization come June. That said, we have already expressed a willingness this offseason to sacrifice a pick for the right guy with the right terms.”

The Colorado Rockies at some point will likely trade outfielder Carlos Gonzalez this season, but the timing of that may not sync up with the White Sox’s timetable. The free-agent market is still a factor in the spring training mix.

“The notion we are hesitant to jump into the market is not entirely accurate,” Hahn said. “Whenever you are negotiating a contract, regardless of what time of the year, it takes a meeting of the minds on both sides. That does not always happen. I don’t think being hesitant to make a move is one of those factors.”

The White Sox will add depth to this club. As to when that will happen? That’s anybody’s guess.

Bruce Levine covers the Cubs and White Sox for 670 The Score and CBSChicago.com. Follow him on Twitter @MLBBruceLevine.