Villanueva went 7-7 with a 4.16 ERA in 38 games last season, 5-7 with a 4.50 ERA in 16 starts, splitting time as a reliever and a starter.
Entering the free-agent market for the first time Villanueva made it clear that he wanted to be a starter.
The deal is for two years and $10 milllion.
Jackson went 10-11 last season in 31 starts for the Washington Nationals pitching to a 4.03 ERA.
A deal with Jackson would likely include multiple years.
Jackson is said to have narrowed his choices between the Cubs and Texas Rangers.