Shields has multiple offers in hand and is expected to sign before the end of this week, major-league sources told FOX Sports.
It's not known which teams have offered Shields a contract, but rival team executives said Tuesday they believe the San Diego Padres and New York Yankees have been in recent contact with Shields' agent, Page Odle.
Shields, 33, is the last major free agent left on the open market. He has thrown the most innings in the major leagues over the past eight seasons and is coming off a year in which he posted the third-best ERA+ of his career.
Shields rejected a one-year, $15.3 million qualifying offer from the Kansas City Royals in November. Ken Rosenthal of FOX Sports reported in early January that two major-league team executives believed Shields had a five-year, $110 million offer. Shields apparently rejected that proposal and may have little choice but to sign for less money now. No free-agent pitcher has signed a contract in excess of $50 million after Feb. 1 of a given year.