Since the D-backs acquired third baseman Chris Johnson on Sunday, speculation has intensified that they could deal shortstop and free-agent-to-be Stephen Drew.
Towers declined to answer when asked if he was getting a lot of calls on Drew.
"I really don't want to get into names and discussing actual names that we're talking about," Towers said. "All I would say is that we have currently [players] on our 25-man [roster] that people have asked about, as well as prospects, and we're looking at every other organization really with the purpose to improve our 2012 club if we can."
Drew had a closed-door meeting with manager Kirk Gibson on Monday afternoon, but both men said it was not a trade-related discussion.
Drew, meanwhile, continues to try and tune out the rumors.
"It wasn't no trade talk kind of stuff," he said of the meeting. "If something happens, it happens, then we'll know more about it. Other than that I'm still with Arizona and just going to prepare for tonight. We're still in the battle here."
As has become clear for a while now, it is unlikely that outfielder Justin Upton will get dealt before the Deadline.
"All I can tell you I have had no dialogue about Justin Upton today or yesterday," Towers said. "I think clubs have a pretty good feel that at this point in time we're 4 1/2 games out, and he's a big part of our ballclub. But I would say unless something drastically changes in the next 24 hours that Justin Upton is going to remain here."
Towers also reiterated that the club is not planning on dealing any of its top prospects -- such as Trevor Bauer or Tyler Skaggs -- and in most deals the D-backs are looking at getting back pitching.
"I think the roster as it is, is OK," Towers said. "But if we feel like we can improve it in other ways, we're certainly going to look at it."