If that's the case, Colin Kaepernick is the most qualified option on the market.
He's also the most controversial.
Kaepernick took a knee during the national anthem last year, starting a wave of protests in response to police shootings and racial inequality across the United States.
Over his six years in the NFL, Kaepernick has both led his teams to deep playoff runs, and been benched for poor performance. But at least recently, he still appears to be a productive quarterback. In the 2016 season, he threw for 2,241 yards, 16 touchdowns and four interceptions in 11 games. He also rushed for 468 yards, adding two more touchdowns on the ground. The team went 1-10 in his starts.
His actions drew mixed responses from around the league and the country.
Criticism of Kaepernick came from as high up as President Donald Trump, who connected NFL owners' hesitation to sign him with fear of potential backlash from his Twitter feed.
"It was reported that NFL owners don't want to pick him up because they don't want to get a nasty tweet from Donald Trump," Trump said in March. "Do you believe that? I just saw that. I just saw that."
But Kaepernick is still popular with many fans. His was the 17th-most sold NFL jersey in May 2017, even while remaining unsigned, ahead of stars like Matt Ryan, Drew Brees and Cam Newton.
The Colts are no stranger to controversial players on their roster. After a long time of trying to do things "the right way," the team has taken risks on players who have brought off-the-field distractions.
Just last year, Colts' cornerback Antonio Cromartie kneeled before two games, as part of the same protest that Kaepernick started.
"I'm a black man first," Cromartie said.
He further explained his reasoning by saying he has six young, black sons.
"Why wouldn't I speak up for them, and speak up for the other young black men who are growing up?" Cromartie said. "Why wouldn't I take a stand for any of that? That's what it's all about. We're trying to make change."
He was released the week after his second protest. Coach Chuck Pagano said it was a football decision, but Cromartie's wife believed it was because of his actions during the national anthem.
"[O]ne things for sure I know my husband was told Not to take a Knee and he went with his heart and he took one," she said, in part, in a Instagram post. "And that cost him his Job.. and Clearly this Statement backs that up"
Team owner Jim Irsay hasn't spoken about Kaepernick specifically, but he has voiced his displeasure about the distraction the former 49ers quarterback brought to the league.
"It hasn't been a positive thing," Irsay said. "What we all have to be aware of as players, owners, PR people, equipment managers, is when the lights go on we are entertainment. We are being paid to put on a show. There are other places to express yourself."
Kaepernick's actions, while controversial, never extended into a criminal problem, as the Colts have at times recently dealt with.
A recent study shows Colts players have had 34 arrests since 2000, which ranks tied for sixth among all NFL teams.
One of the most notable recent arrests of Colts players was defensive lineman David Parry. Parry, who started every game for the Colts over the last two years, was arrested in Arizona in February on preliminary charges of auto theft, robbery, resisting arrest, driving under the influence and criminal damage.
While being arrested, Parry antagonized the police officers, used gay slurs against them and called them "fat f---s," ESPN reported.
Parry eventually pleaded guilty to one count of disorderly conduct and one count of attempted unlawful means of transportation. He was sentenced to two years of supervised probation. He remains on the roster.
A former Colts linebacker, Andrew Jackson was arrested twice in one year on DUI charges, once in Muncie, Indiana, and a second time in Louisville. The Colts cut him about a month after the second arrest.
If it turns out the rumors prove true, and Luck is out longer than what is currently said, look for the Kaepernick-to-Indianapolis discussions to pick up. Whether or not they'd want to sign somebody who could alienate part of the fanbase is the bigger question.