Villarreal has remained with the team. Manager Jim Leyland did not want to comment further about the matter, saying Sunday: "The less said, the better."
Villarreal went 3-5 with a 2.63 ERA last year in 50 appearances. The 25-year-old right-hander struck out 66 hitters in 54 2-3 innings.
Security back home has been a concern in recent years for Venezuelan players and their families because of a rising wave of kidnappings.
In June 2009, Colorado Rockies catcher Yorvit Torrealba's 11-year-old son and brother-in-law were kidnapped and released a day later.
The mother of former pitcher Ugueth Urbina, a two-time All-Star, spent more than five months in captivity until she was rescued in early 2005.