Lovullo has spent the last two seasons with the Red Sox and he doesn't have any big league managerial experience. However, Lovullo was a minor league manager for nine seasons compiling a 661-609 record with the Cleveland Indians and Red Sox organizations where he led teams to four postseason appearances and two league titles.
Lovullo played eight seasons in the big leagues with seven teams before retiring after the 2000 season while playing in Japan.
The Rangers have interviewed with three candidates overall, including two in-house in pitching coach Mike Maddux and Triple-A manager Steve Buechele.
Rangers officials plan to conduct more interviews this week including with interim manager Tim Bogar.