Eppler and the Angels are currently looking to round out their pitching staff, having addressed a few holes on offense. It's possible that those plans could eventually include Weaver, who has spent all 11 of his Major League seasons with the Angels.
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But after discussions with the veteran right-hander, the two sides have agreed to let free agency play its course. They'll allow the market to settle before pursuing a deal.
"We've had conversations," Eppler said on Tuesday from the General Managers Meetings. "We even met in person, actually spent time together and talked a little bit about free agency, talked about the club, the direction on both of our parts -- what direction he wants to go, what direction we're going to go.
"We kind of walked out of that saying, organically, we're just going to allow the offseason to take shape first before meeting up again."
Weaver posted a career-high 5.06 ERA in 178 innings in 2016. He enters a thin class of free-agent starters, coming off the worst season of his career.
As for the notion of Weaver pitching elsewhere, Eppler knows it's a strange one.
"From people involved with this club for a lot of years -- and people in my situation, who have been with the club for one year, but have watched him over the course of his career -- yeah, there's no doubt. It'd be unique to see him in a different color, in a different uniform," Eppler said.
Weaver isn't the only question mark in the Angels' 2017 rotation. The biggest is right-hander Garrett Richards, who hasn't pitched since May.
Instead of having Tommy John surgery on a torn ligament in his right elbow, Richards opted for stem cell therapy and rehab.
"Everything seems pretty good right now and pretty positive," Eppler said. "He'll come back to L.A. in the next few weeks ... and see our docs, get another update and see where he's at. Everything's been pretty positive so far."
Richards' presence would give the Angels' rotation an instant boost. Over the past three seasons, he's posted a 3.11 ERA with a .222 batting average against.
Behind Richards, Tyler Skaggs is in line for an innings limit in 2017, and Eppler will discuss those specifics in the next few weeks. The 25-year-old left-hander was briefly shut down in September with elbow trouble, but tests revealed no structural damage.
As for the Halos' external rotation options, they'll do their due diligence in the slim starting-pitching market.
"I think we'll be able to pull guys in that have at least been starters at some point in their careers or have the ability to start," Eppler said. "We'd like to add as many [starters] as we can take but not completely handcuff any flexibility."