Parra, who hit .292 and won a Gold Glove in left field for the D-backs last season, will see his playing time markedly reduced this year after the club signed free agent Jason Kubel to a two-year deal.
Towers did say that his scouts have heard from other scouts that their clubs would have an interest if the D-backs ever decide to move Parra.
"I haven't had any discussions," Towers said. "I still see him very much a part of this club. Having a great spring, performing well, he's working his rear end off, he's played well. No discussions about him."
If the D-backs do make a deal at some point they will target catching especially with Miguel Montero and the D-backs recently tabling contract negotiations. Montero will be a free agent after the season.
Don't look for the D-backs to part with top pitching prospects like Tyler Skaggs, Trevor Bauer or Patrick Corbin either.
"They haven't really brought those pitchers up," Towers said of other team's GMs. "Because they know we want to hang onto them right now."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.