The calls were made before the trade deadline and prior to the Colts placing Luck on injured reserve following complications associated with his ongoing rehabilitation from shoulder surgery.
"Look, we had some calls last year at the trade deadline," Ballard said on Saturday. "And I just -- come on man. I'm not taking those seriously.
"We're not trading Andrew Luck. I'm not putting that on my resume."
Colts owner Jim Irsay told reporters earlier on Saturday that the team was never seriously intrigued by any offer for Luck.
"Trust me, there were people that would've given an unprecedented amount of draft picks, all with a No. 1 [pick] behind them, for him, and we wouldn't even think of drifting in that direction," Irsay said. "He's our guy. We feel 100 percent confident that he is going to come back and lead this football team with some of the new teammates he's accumulated to great things."
Irsay declared last month that Luck had "turned the corner" in his rehab after the latter missed all of last season as he rehabbed his surgically repaired shoulder.
"I think it's a stepping-stone process," Irsay said. "He's got to go through practices; he's got to get roughed up a little by his teammates; he's got to get roughed up in preseason; and then he's got to play regular season when it's all on the line. You guys know this is a process, and football players like [New Orleans Saints quarterback] Drew Brees have come through for a decade and have had excellence after the surgery that Andrew went through.
"We feel we have a guy for the next 10 years who's going to be a great, great football player."
After appearing in just seven games in 2015 due to injuries, Luck was coming off perhaps his best overall performance in his six-year NFL career in 2016. He completed 346-of-545 passes (63.5 percent) for 4,240 yards with 31 touchdowns and 13 interceptions. He also ran 64 times for 341 yards with two more scores.
For his career, Luck -- the No. 1 overall pick in the 2012 draft and a three-time Pro Bowl selection -- has completed 1,570 of 2,651 passes (59.2 percent) for 19,078 yards with 132 touchdowns and 68 interceptions. He has 286 rushing attempts for 1,442 yards and 14 more touchdowns.
Last season, the Colts finished 4-12 with Jacoby Brissett starting 15 games at quarterback. Brissett completed 58.8 percent of his passes while throwing for 3,098 yards and 13 touchdowns with seven interceptions.
The Colts are 43-27 with Luck under center during the regular season, and they are 10-16 when he does not play.