Towers spent 14 seasons as San Diego's GM from 1996-2009, and he has been Arizona's GM since '10. Two months ago, the D-backs hired Tony La Russa in a newly created role as the team's chief baseball officer.
Fowler said by email late Thursday that the Padres haven't contacted the D-backs about obtaining permission to talk to Towers.
"I know [him] and like him … he has had a great relationship with many people in all areas of the Padres' organization," Fowler said. "That said, we have not asked for permission from the D-backs to talk to Kevin. I don't know how this story got started."
The Padres, who relieved Josh Byrnes of GM duties on June 22, reportedly have narrowed their general manager candidate list to four, and all will return to San Diego next week for a second interview.
According to Scott Miller of Bleacher Report, Red Sox assistant GM Mike Hazen, Yankees assistant GM Billy Eppler, Rangers GM A.J. Preller and Kim Ng, the senior vice president of baseball operations for Major League Baseball, are the final four.
Fowler has indicated that he would like to have a new general manager hired by early August.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.