While it's uncertain whether Thomas' deal is for three years or two with an option, a source said the total value could exceed $30 million.
The agreement is contingent upon Thomas passing a physical exam.
Thomas, a two-time American League MVP with the Chicago White Sox, played for a base salary of $500,000 this season, plus $2.6 million in incentives, after coming back from an ankle injury. Oakland made a two-year offer to Thomas before the season ended.
A's assistant GM David Forst, the team's representative at the meetings, declined to comment on the Blue Jays' pursuit of Thomas.
Thomas would represent a significant power upgrade at the DH position for Toronto. Shea Hillenbrand, Frank Catalanotto, Eric Hinske, Gregg Zaun and Bengie Molina assumed the bulk of the at-bats at the position last year, and the Blue Jays finished tied for 12th among American League clubs with only 16 home runs out of the designated hitter spot.
Thomas finished last season with 487 career homers. Barring injury, he will become the 21st player to join baseball's 500 home run club early next season.
Jerry Crasnick covers Major League Baseball for ESPN Insider. Information from The Associated Press was used in this report.