"The spirit of [negotiations] was, we're in this together and as long as Philip wants to play, wants to be here," Reich said Monday, per Mike Wells of ESPN.
"It's the NFL, we know he has to prove it. We have to prove it as a team to keep him wanting to play. I can just tell you from the previous relationship [with the Chargers], I really believe it's Philip's intent to play multiple years. I personally believe he's more than capable of multiple years."
Rivers had spent his entire 16-year career with the Chargers, making 224 straight starts since taking over under center in 2006. Reich worked with the veteran from 2013-15, first as a quarterback coach and then as offensive coordinator.
The familiarity could help lead the Colts to more success in 2020 after a disappointing 7-9 season last year. The eight-time Pro Bowler will try to be an upgrade over Jacoby Brissett, who had an up-and-down season after Andrew Luck's sudden retirement.
However, Rivers is coming off a disappointing showing in 2019 with 23 touchdowns and 20 interceptions, third-most in the NFL. His 88.5 quarterback rating was his second-lowest since 2008.
It allowed the Chargers to move on from the free agent, eventually selecting Justin Herbert with the No. 6 overall pick in the 2020 draft.
Rivers believes he can still contribute, but the 38-year-old doesn't know exactly how long for.
"If I feel like I feel right now next year, then I'll be excited to keep going," he told Andrew Walker of the team's official site in March. "Again, depending on how the team feels about that and etc. So, I don't know, I don't have a number on it."
Rivers wants to coach his oldest son when he reaches high school, but he's currently 12 years old.
The Colts invested in the future by taking Jacob Eason in the fourth round of the draft, someone who could take over the starting job down the line. With Rivers, Brissett and Chad Kelly all set to be free agents after the 2020 season, his time could come soon.