By Bruce Levine-

(CBS) While the Cubs and White Sox figure to chase some combination of top free agent pitchers James Shields, Jon Lester and Max Scherzer this offseason, it’s also worth discussing another subplot. Who are realistic options for the two teams if the big three slip through their hands? Because both Chicago teams are in dire need of additions to the upper tier of their rotations in 2015.

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Although it appears the Cubs may have a relationship with and city advantage in signing Lester, let’s presume for this written exercise that a team closer to winning the World Series outbids the Cub brass for Lester’s services.

After the top three on the market, the quality of pitchers begins to drop down. All the aforementioned aces will be receiving contracts from five to seven years with a $20-million minimum per season. (Scherzer already scoffed at a six-year, $144-million offer from the Tigers last spring, which was figures to $24 million per season.) Knowing that the top three might wait until one establishes market price, both Chicago teams may have to strike early in the secondary starters’ market.

A couple pitchers who make sense for both sides of town, including right-hander Justin Masterson — though how to read his up and down trends is a bit difficult. At his best, Masterson is a No. 2 to No. 3 starter on an average-to-good staff. He’ll turn 30 in 2015. A less-than-stellar 60-72 career mark and a 4.24 ERA doesn’t jump out at you with a “must sign” flashing around his name. Despite the rote numbers being coming up flawed, real diamonds in the rough have been made whole by top-shelf pitching coaches with the Cubs and White Sox. The respective front offices believe that the Cubs’ Chris Bosio and White Sox’s Don Cooper can take an underachiever like Masterson and find a pitch or new confidence level to turn him around.

Masterson was mediocre in 2014, going 7-9 with an ugly 5.88 ERA. Pitching for both Cleveland and St Louis, he was dropped to mop-up bullpen duty in September for the Cardinals.

“I saw him shut down the Marlins with some very nasty stuff in August,” a National league advance scout said of Masterson allowing just three hits in seven innings. “He had a sinker that was hitting the bats like cement doors that day. The next time or two out, he struggles with his command. It’s very perplexing.”

Masterson was signed and developed by the Red Sox when current Cubs front office members Theo Epstein, Jed Hoyer and Jason McLeod were all in Boston. He was traded by Epstein to Cleveland on July 31, 2009, along with two other players for Victor Martinez. His breakout campaign was in 2011, when he went 12-10 with a 3.21 ERA.

After a poor season in 2012, he rebounded with a 14-10 mark and 3.45 ERA in 2013. Once again inconsistent early this season (4-6 with a 5.51 ERA with Cleveland), the Indians sent him to the Cardinals for James Ramsey at the trading deadline.

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With one more consistent season in 2014, such a pitcher with Masterson’s track record would have been looking at a four-year, $60-million deal at the minimum. Instead, he’ll more than likely have to prove his worth again with a shorter-term deal. Masterson made $9.76 million last season. He has potential value to both teams, as both are in real need of 200-inning pitchers.

The White Sox must get a right-handed starter to go with a rotation that will more than likely have four lefties in it. The Cubs still are looking to add innings eaters at the rotation level. From the list of starters who ended the year in the Cubs’ rotation (no, Edwin Jackson doens’t count), only Travis Wood has thrown at least 200 innings in a season.

The other pitcher who may fit well for the two Chicago teams is former Cubs right-hander Jason Hammel. Now 31, Hammel signed a one-year, $6-million contract with the Cubs before the 2014 season. He was told by Epstein that there was a better-than-average chance he would be moved for more youth at some point of the season.

“The Cubs people were very transparent about the deal,” Hammel told me in September. “It was a great experience pitching there and yes, I would certainly consider going back if everything worked out.”

Hammel pitched his best ball in April and May for the Cubs and in September for Oakland. During those three months, he had an 8-4 record with an ERA under 3.00. August was a train wreck for the affable pitcher, who went 1-4 with a sky-rocketing ERA of 7.82 after he and Jeff Samardzija were dealt to the A’s.

A three-year, $30-million contract might be a bargain for Hammel despite his career 59-70 record. Hammel is a fourth starter and could be a very good one for the team who signs him after free agency begins in early November.

While neither Masterson nor Hammel is a sexy name, both could be solid additions to the staffs of the Cubs or White Sox.

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