The Cubs added to their rotation with the signing of right-hander Tyler Chatwood to a three-year deal Thursday, but there are still more valuable innings that need to be filled with Jake Arrieta and John Lackey shopping their talents in free agency. With that in mind, the Cubs are continuing their strong push to sign free agent right-hander Alex Cobb, sources said. The rumors on a Cobb-Cubs marriage have been out there for several months, and with the Winter Meetings starting Monday, Chicago would like land Cobb as quickly as possible to avoid any traps and new suitors that may await in the next week. Agreeing to a deal with Cobb before Monday would also give the Cubs more leverage during the Winter Meetings because they wouldn’t be as desperate to fill a rotation spot. In the Cubs can add the 30-year-old Cobb on a multi-year deal in the coming days, they would have five starting pitchers under team control for three more seasons. Jon Lester, Jose Quintana, Kyle Hendricks and Chatwood all have contracts that run through 2020, and any deal for Cobb would be at least that long. The Yankees are believed to be the main competition to the Cubs for Cobb, who has spent his entire big league career with the Rays and who went 12-10 with a 3.66 ERA and 1.22 WHIP. A four-year deal is assumed to be the end game for Cobb’s services. Adding Cobb would give the Cubs some breathing room as they look to develop young pitchers at the lower levels of the minor leagues. Some of those top prospects are right-hander Jose Albertos, right-hander Adbert Alzolay, right-hander Oscar De La Cruz, right-hander Alex Lange and left-hander Brendon Little. Cobb has a great relationship with new Cubs pitching coach Jim Hickey, who mentored Cobb for six season in Tampa Bay. Joe Maddon was also Cobb’s first manager in the big leagues.