Montero will be a free agent at the end of the season and both sides said toward the end of Spring Training that negotiations on an extension had not progressed far enough along for a deal and they would hold off talking until the end of the regular season.
CBSsports.com's Jon Heyman reported Wednesday that negotiations could begin soon.
Montero said before Wednesday's game that he had not heard anything about that.
D-backs general manager Kevin Towers, though, left the door open to the possibility.
"We agreed with Miggy and his agent that we'd give it until the end of Spring Training, and if nothing happened then, we're certainly open throughout the season if he feels like he's comfortable," Towers said. "But any negotiations that we have, both sides decided to keep it confidential."
Towers declined to say whether the club would in fact make a proposal to Montero.
"I don't want it to be a distraction for Miggy," Towers said. "If we end up coming to terms then you guys will know. If we don't, nothing ever happened. Any dialogue that we have or if it opens up again we're going to probably keep all that confidential."