San Francisco 49ers general manager John Lynch sat down with reporters on Monday for his annual pre-draft press conference. The media session wasn't just for draft-related questions. Lynch also discussed the futures of three players who were with the team last year.

DeForest Buckner's contract extension

The 49ers have started contract extension discussions with their budding defensive star, DeForest Buckner. Those discussions, however, are in their infancy.

"We've had conversations here and there," Buckner told reporters last week. "Honestly, it's just very early, just because I'm eligible for a new contract going into my fourth year. It's still very early in the process."

The 49ers have until May 3 to decide if they should exercise Buckner's fifth-year option. Of course, agreeing on an extension before that deadline would make the option unnecessary. And the team could continue discussions after that.

"I would love nothing more than for DeFo to be here," Lynch said. "We've got a long time to work on that. He's very important to us, and he's another guy who's a big part of what we're doing. I just love everything about him, and the way he goes about his business. I think he's a special player, and we'd like to keep him here for a long time."

Joe Staley's NFL future

Veteran tackle Joe Staley, who is entering his 13th NFL season, has expressed an interest in playing beyond the 2019 season. This year, however, is the final one in his current contract.

Staley has also stated in the past that he has no desire to play elsewhere. He has spent his entire NFL career with the 49ers, who drafted him with the No. 28 overall pick in 2007.

"We all know what he's meant to this organization," Lynch said. "He's got a unique opportunity to be part of this organization and my hope is that he only plays for one organization. I think he's a special player. He's a special personality.

"I'm not going to get into the specifics of the contract and where we're going on all that. I'll just tell you that my hope, that Kyle's (Shanahan) hope, that everyone associated that is involved in these decisions, is that Joe never plays anywhere else but the San Francisco 49ers. We're very pleased with Joe Staley and the way he's playing."

Robbie Gould's status

Kicker Robbie Gould is one of three players who are not with the team during this voluntary portion of the offseason program. The other two are new pass rusher Dee Ford and guard Mike Person, who are each an expectant or new father.

Gould has not yet signed his one-year franchise contract and was not expected to report to the 49ers last week. While the franchise tag kept him from leaving the team, he and the 49ers hope to work out a new long-term deal. Lynch and Shanahan want him back and expect him to be handling kicking duties when the team kicks off the regular season in Tampa, Florida on September 8.

"Robbie's going to be a part of us this coming year," Lynch said. "I know that. We would like it to be longer than that, and we've made an attempt to make that happen. We haven't come to an agreement as of yet, and we'll see where that goes.

"Robbie will be a part of us this coming year, and we're excited for that because he's very good at what he does. And he's also a big part of this team."

So why did the 49ers pursue veteran kicker Stephen Gostkowski, who re-signed with the New England Patriots?

"The thinking was we've got to do our due diligence in terms of being prepared for all scenarios," Lynch responded. "Stephen was a free agent, and also very good. Our number one priority in that respect was to try to figure out something with Robbie.

"Stephen was there. I think our interest quickly got the Patriots to lock him down, and that's where he's at, so I'll leave that at that."

Meanwhile, Gould remains in Chicago with his family.

"Robbie's a guy who works extremely hard at his craft," Lynch said. "By virtue of that position, he can do that wherever he is. He can do it in Santa Clara. He can do it in Chicago."