By Bruce Levine–

CHICAGO (CBS) — The number of teams ready to sign free-agent outfielder Yoenis Cespedes appears to be down to five. With the signing of 28-year-old Justin Upton to a six-year $132-million contract Monday, the Tigers are now out of the Cespedes sweepstakes.

Locally, the question is this: Will the Chicago White Sox sweeten their initial offer to the power hitter?

The White Sox, Angels, Astros, Mets and Braves appear to be the final clubs that have serious interest in signing the 30-year-old Cespedes, a Cuban native who hit .291 with 35 homers, 105 RBIs and a .942 OPS in 2015. The White Sox have previously offered a three-year contract, but that fell short of the five- or six-year deal that Cespedes desires, according to industry sources.

Upton’s deal averages $22 million annually and includes an opt-out clause after two contract years are completed. Earlier in the offseason, outfielder Jason Heyward signed an eight-year, $184-million deal with the Cubs, for an average of $23 million annually. Heyward, 26, has opt-out clauses after the third and fourth years of his deal.

The Angels have mostly platoon players to roam left field. The fact that first baseman Albert Pujols may start the season on the disabled list could influence owner Artie Moreno to write a big check.

In Houston, the Astros have little payroll committed in 2016 or 2017. The Mets and Braves appear to be offering shorter-term deals of the one- or two-year variety.

This sets the stage for the White Sox to hit a home run on the free-agent market. Chicago could tweak a three-year offer to four seasons with an opt-out clause after the second and third years so that the sides can reach a middle ground.

The White Sox are clearly in a two-year win-now window. Newly acquired infielders Todd Frazier and Brett Lawrie are free agents after the 2017 campaign, and left fielder Melky Cabrera’s deal runs through the same season for $14 million annually. New catchers Alex Avila and Dioner Navarro are signed to one-year deals.

The White Sox have significant payroll coming off the books after 2016 in the form of left-hander John Danks ($16 million in 2016) and first baseman/designated hitter Adam LaRoche ($13 million).

With Alex Gordan back in Kansas City and Upton joining Detroit, it would appear the White Sox need to answer with a strong move to challenge for the AL Central title in next season. It’s possible the White Sox could go the trade route and get one of the Rockies’ hitters who should be on the trade market — Carlos Gonzalez, Corey Dickerson or Charlie Blackmon. A left-handed bat from that group would give the Chicago lineup better slugging balance in 2016.

Cespedes won’t cost any team that signs him a draft pick because he didn’t spend the entire 2015 with one club. He was shipped from the Tigers to the Mets just before the trade deadline.

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