Shields will reportedly make a decision about which team he will join by the end of the week.
After helping the Kansas City Royals reach the World series in 2014, Shields rejected the team's one-year, $15.3 million qualifying offer.
Shields, 33, posted a 3.21 ERA with 180 strikeouts and 44 walks over 227 innings during the the 2014 regular season.
The Cubs went 73-89 and finished in last place in the National League Central this season.
In December, the Cubs signed free-agent pitcher Jon Lester to a six year, $155 million contract.
Again, everyone getting excited but R-E-L-A-X. They're simply kicking the tires. No deal close. Shields could make his decision this weekend— David Kaplan (@thekapman) February 5, 2015