Lannan was twice the Nationals' opening day starter, Flores was once viewed as the team's catcher of the future and Gorzelanny was a productive long reliever during the Nats' 2012 playoff run.
All three would be free agents if they are indeed non-tendered.
Teams have until 11:59 p.m. tonight to offer arbitration-eligible players a contract for next season. Because the Nats haven't officially made any moves with Lannan, Flores or Gorzelanny, nothing is set in stone. A trade involving one or more of these players could still be worked out or the Nats could, of course, have a late change of heart.
The Nats were expected to tender contracts to seven arbitration-eligible players: shortstop Ian Desmond, starters Jordan Zimmermann and Ross Detwiler, relievers Drew Storen, Tyler Clippard, and Craig Stammen and outfielder Roger Bernadina.
Lannan has gone 42-52 with a 4.01 ERA over six seasons with the Nationals. The 28-year-old led all Nats pitchers with 10 wins in 2011 but was beat out for the final spot in the rotation by Ross Detwiler just prior to the start of the 2012 regular season.
Lannan spent the bulk of this season at Triple-A Syracuse, but he was a factor for the Nationals down the stretch, going 4-1 with a 4.13 ERA in six big league starts.
He has been one of the organization's longest-tenured players, but if he is non-tendered, he would get a fresh start and should receive plenty of interest from pitching-needy teams.
Flores batted .213 with six home runs and 26 RBIs in 83 games this season. He threw out nine of 60 runners attempting to steal, a 15 percent caught-stealing rate.
Gorzelanny potentially being non-tendered is a bit of a surprise given that he was set to be the only left-handed reliever from the Nationals' 2012 roster under contract for 2013. Sean Burnett and Michael Gonzalez are also free agents, as is Zach Duke, who spent much of the season starting at Triple-A Syracuse, but joined the Nats after rosters expanded in September and worked out of the bullpen.
The 30-year-old Gorzelanny went 4-2 with a 2.88 ERA in 72 innings this season. He made $3 million in 2012 and was set to make slightly more than that in arbitration this offseason.
The Nationals could still negotiate new deals with any of the three players if they are non-tendered, but Gorzelanny is the only one they'd likely consider trying to bring back at a lesser salary at this point.
Update: Lannan, Gorzelanny and Flores have indeed been non-tendered, according to the transactions page at MLB.com.
Those three are now free agents.