By Bruce Levine–

CHICAGO (CBS) — The White Sox have added two new infielders to their team in the last few weeks in third baseman Todd Frazier and second baseman Brett Lawrie. Whether they will add a shortstop remains unknown at this point.

Former White Sox shortstop Alexei Ramirez is still a free agent in limbo at this juncture, and the team hasn’t completely closed the door on bringing the 34-year-old veteran back.

Still, the consensus opinion right now is that Chicago will put the rest of its payroll resources into a free-agent outfielder. The names of Alex Gordon, Justin Upton and Yoenis Cespedes have all been connected in discussions with the club. The payroll commitment for 25-man roster currently stands around $110 million. How much more chairman Jerry Reinsdorf wants to give to the baseball department is mere conjecture at this time. Reinsdorf can be unpredictable when it comes to delving out big money for free agents.

If the White Sox opened the 2016 season today, second-year pro Tyler Saladino would be the starting shortstop, according to general manager Rick Hahn. That could change if the team decides to bring back Ramirez, a durable Cuban who was consistent for his first seven seasons in a White Sox uniform.

The first half of 2015 was a different story for Ramirez, whose average was still below .200 in early May and who hit .224 prior to the All-Star break. His second half was much better, as Ramirez came close to his career slash lines. Still, his range factor on defense seemed a tad off all season as well.

The White Sox held a $10-million option on Ramirez for 2016 but declined it and paid $1 million as a buyout.

Ramirez has averaged 157 games played over the last six seasons. He had his best season in 2014, going to the All-Star Game and winning a Silver Slugger award after hitting .273 with 15 homers and 74 RBIs.

The only other free-agent infielder who the White Sox may also look at is Ian Desmond, a decent defender who’s coming off of an off-year much like Ramirez. A 30-year-old former Nationals shortstop, Desmond has had way too many strikeouts the last two seasons (183 in 2014 and 187 in 2015). Those strikeout numbers were about 45 percent higher than his previous four-year average.

The White Sox need to add quality on-base percentage players. The potential addition of Desmond would be counterproductive in that area, as he has a career .312 on-base percentage.

It’s also worth noting the White Sox believe top prospect Tim Anderson will be ready to play shortstop in the big leagues by 2017.

The Padres are looking at adding a linchpin for their infield defense and are checking into Ramirez on a short-term deal. With that in mind, the question still remains: Wouldn’t the White Sox be smart to re-sign Ramirez?

A two-year contract for Ramirez would certainly match up with the other contracts and free-agent status of the White Sox’s position players. The money directed at shortstop wouldn’t be much of a strain on the payroll moving forward, and a creative deal with deferred payments may also allow the team to sign a big-time outfield free agent as well.

Saladino is a nice player who played third base (49 games) and shortstop (11 games) well last season. Still, the fact that Saladino hit .225 with a .602 OPS must be factored into the equation moving forward. Playing every day without missing games like Ramirez has at the most crucial position on the field while generally being an offensive contributor shouldn’t be taken for granted.

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