GREEN BAY, Wis. -- The Green Bay Packers still believe Aaron Rodgers will play for them in 2021, and perhaps beyond. They have no plans to trade him.

That was general manager Brian Gutekunst's message late Thursday night following the first round of the NFL draft, which came after sources told ESPN's Adam Schefter earlier in the day that Rodgers has become so disgruntled with the team that he has told some members of the organization he does not want to return to the Packers.

"We've been working through this for a little while now, and I just think it may take some time," Gutekunst said. "But he's a guy that kind of makes this thing go. He gives us the best chance to win, and we're going to work towards that end."

Rodgers, 37, is under contract through the 2023 season but has no more guaranteed money left on his deal. Gutekunst said the lines of communication with Rodgers and his representatives have been open throughout the offseason, and the two sides spoke again Thursday.

Gutekunst, a fourth-year general manager, denied that the Packers ever told Rodgers they would trade him and reiterated that they have no plans to do that.

"We're not going to trade Aaron Rodgers," he said.

Gutekunst said he did not speak with San Francisco 49ers general manager John Lynch on Thursday about a deal for Rodgers. Lynch told reporters Thursday that the 49ers "inquired" about Rodgers, but he did not say when that took place and added, "It was a quick end to the conversation; it wasn't happening."

Gutekunst said it wasn't like the phones were ringing off the hook at Lambeau Field after the news of Rodgers' unhappiness broke.

"Sometime after 5 o'clock, after a lot of the stuff had kind of hit the airwaves, I got I think one call," Gutekunst said. "It was very brief, and that was it."

Earlier this offseason, the Los Angeles Rams reportedly called to inquire about Rodgers' availability via trade before they dealt for Matthew Stafford.

"I'm not gonna confirm that," Rams GM Les Snead said Thursday. "But I don't think he was ever available."

Part of Rodgers' unhappiness stems from last year's draft, when the Packers did not inform him of their decision to trade up and draft his potential replacement, Jordan Love, at No. 26 overall, sources told Schefter.

"I certainly look back to last year's draft and just kind of maybe some of the communication issues we could have done better," Gutekunst said. "There's no doubt about it. The draft's an interesting thing. It can kind of unfold differently than you think it's going to unfold, and it happens pretty fast. But certainly, I think, looking back on it sitting where we sit today there could have been some communication things we did better."

Despite being rebuffed by Rodgers in their attempts to extend his contract, the Packers still believe they can convince him to come around. They brought back all but two starters from their 13-3 team that reached the NFC Championship Game for the second straight season.

"I'm not going to speak for Aaron, but I think obviously we have a really good team and I do think he'll play for us again," Gutekunst said. "And like I said, we're going to work towards that and we've been working towards that on a number of different fronts. The value that he adds to our football is really immeasurable, you know what I mean? He brings so much to the table not only as a player but as a leader. He's so important to his teammates, to his coaches, so yeah, that's the goal.

"I think we obviously have a very good football team here, we have a great organization, we're very committed to him and I think as the lines of communication have been open, I'm just optimistic that that's what's best for the Green Bay Packers and I truly believe that's what's best for Aaron Rodgers, as well."

Gutekunst was the only member of the Packers organization to speak to reporters on Thursday after they drafted Georgia cornerback Eric Stokes at No. 29 overall. Coach Matt LaFleur is scheduled to take questions following the draft on Saturday.

"I think it's like everything in this business. Look, I don't think anything ever surprises you," former Packers coach and current Cowboys coach Mike McCarthy said Thursday. "And things like that go on. Conversations, I think, are always going on when it comes to player acquisition. Obviously no one knows the impact that Aaron Rodgers has made on the Green Bay Packers [more than McCarthy] but, yeah, I haven't given it much thought. Obviously I didn't see anything happen today, so ... good news story."

Gutekunst wouldn't put a deadline on when the Rodgers situation needs to be resolved for it not to impact the 2021 season.

"It's kind of a hypothetical and it's kind of, like I said, our desire is to have Aaron as our quarterback leading this team and competing for championships," he said. "So, it's a little bit hypothetical, so we'll get to that. We'll cross that bridge when we get to it."

ESPN's Todd Archer and Lindsey Thiry contributed to this report.