Elway shared the news on Monday via a video conference call, saying that he has been in "active" negotiations with Simmons' camp and that both sides have submitted offers.
Simmons, who is set to make $12.7 million this season under the exclusive franchise tag, is entering his fifth season with the Broncos and has started 45 games over the last three years. Only Kevin Byard, Tre Boston and Ha Ha Clinton-Dix have more interceptions from the safety position than Simmons' 11 since he came into the league in 2016.
The former third-round draft pick had 93 total tackles, 15 pass breakups and four interceptions last season.
Elway also addressed the health of defensive back Bryce Callahan, who missed all of 2019 due to a series of foot injuries after signing a three-year, $21 million contract last offseason.
"We're hopeful that things are coming along and he'll be ready by the time we get to training camp," Elway said.
If he is healthy, Callahan projects as the Broncos' starting slot cornerback this season.
The video conference call followed the league's virtual draft test run on Monday afternoon in an attempt to identify any technological problems before Thursday's first round.
Front office personnel from multiple teams complained of bandwidth issues that hindered communication early on, but the issues were smoothed out as the test run continued.
"The draft went smooth. It got off to a bit of a hiccup when we first started, but other than that it went really smooth," Elway said.
"There were really no problems with it, so we got more comfortable with it. It should be fine to go without a glitch.
"I'm sure there will be a couple glitches here and there, but actually for the first time I thought it went pretty well."
Denver has 10 total selections in this week's NFL draft, including No. 15 overall, as it looks to build around second-year quarterback Drew Lock. The Broncos have two extra picks in the third round, giving them four selections on Friday.
Flores has launched a class action lawsuit, alleging the NFL is rife with racism and has a "disingenuous commitment to social equity".
In the suit, Flores alleges that when he interviewed for the role of head coach with the Broncos in 2019, Elway and former Denver executive Joe Ellis were late and appeared "completely dishevelled" from an evening of heavy drinking.
Flores is suing the league along with teams from which he alleges he has personally experienced racism, naming the Dolphins and the Broncos along with the New York Giants as defendants, together with "John Doe Teams 1 through 29".
The suit, filed at the United States District Court for the Southern District of New York, demands a jury trial. The NFL said Flores' claims "are without merit", adding that it would put up a defence. The three teams named by Flores have also rejected his allegations.
The NFL has a 'Rooney Rule' in place that requires all teams seeking a new head coach "to interview at least one or more diverse candidates".
It is alleged in the lawsuit that Flores "was interviewed only because of the Rooney Rule" by the Broncos and was never intended to be "a legitimate candidate", while also criticising the interview board.
The Broncos described the various claims against the franchise as "blatantly false" and "baseless and disparaging", to which Flores responded on ESPN's Get Up! show on Wednesday, saying: "I deal in truth, that's my reaction. I deal in truth. Honesty, integrity is important to me, and hopefully, there's a day we find out the truth on that one."
Elway released a statement on Thursday to further deny the claims made by Flores, saying: "While I was not planning to respond publicly to the false and defamatory claims by Brian Flores, I could not be silent any longer with my character, integrity and professionalism being attacked.
"I took Coach Flores very seriously as a candidate for our head coaching position in 2019 and enjoyed our three-and-a-half-hour interview with him. Along with the rest of our group, I was prepared, ready and fully engaged during the entire interview as Brian shared his experience and vision for our team.
"It's unfortunate and shocking to learn for the first time this week that Brian felt differently about our interview with him.
"For Brian to make an assumption about my appearance and state of mind early that morning was subjective, hurtful and just plain wrong. If I appeared 'dishevelled,' as he claimed, it was because we had flown in during the middle of the night - immediately following another interview in Denver - and were going on a few hours of sleep to meet the only window provided to us.
"I interviewed Brian in good faith, giving him the same consideration and opportunity as every other candidate for our head coaching position in 2019."
The Broncos recently appointed Green Bay Packers offensive coordinator Nathaniel Hackett as their new head coach, having parted company with previous head coach Vic Fangio, who was hired in 2019.
Fangio achieved a 19-30 record during his three seasons with the franchise, failing to reach the playoffs throughout his tenure.
