Sanders and LaRue entered the market on Monday, the first day that filing was open after the close of the World Series.
They are among six Royals eligible to file. The others are first baseman Mike Sweeney and pitchers Odalis Perez, David Riske and John Thomson.
The Royals also announced that infielder Andres Blanco had been outrighted to Omaha, taking him off the 40-man roster and making him a free agent.
LaRue was signed last winter as a backup for catcher John Buck after eight years with the Cincinnati Reds. Coming off an injury-plagued season, LaRue did a good job defensively for the Royals and played in 66 games.
However, he had one of the worst seasons on record at the plate. He went just 25-for-169 and his .148 average was the sixth lowest among players with at least 150 at-bats since 1920.
It was a lost season for Sanders, who played just 24 games because of a torn left hamstring. He got off to a .367 start in 16 games, but then was hurt and spent most of the year on the disabled list.
Sanders, 39, has 305 home runs and 304 stolen bases in his 17-year career. After eight years with the Reds, he played for seven other clubs.
Blanco, a fine-fielding shortstop and second baseman, underwent surgery on his left shoulder after the 2006 season. Optioned to Omaha last spring, he played just 28 games and batted .196 before injuring his left hamstring.
While rehabbing at Surprise, Ariz., he injured his right hamstring and missed the rest of the season. In three seasons, he played a total of 78 games for the Royals.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.