3. New Orleans Saints
You may have noticed a trend here that is more than just contending teams that could be an injury away from needing a quarterback. All three teams are in the south and are relatively close to Rivers' home.
Obviously, location won't stop Rivers if a contending team needs a quarterback and he has a legitimate chance of winning a Super Bowl, but it is likely a huge plus for the family man and it helps that there are three teams in the south that could need a quarterback.
The New Orleans Saints are entering an interesting era for the team at the quarterback position. Drew Brees has retired and Jameis Winston has been re-signed to likely get the starting duties.
Tayson Hill is a possibility but he is best used as a swiss army knife, not as the team's every-snap quarterback. There is obviously a lot of risk involved in trusting Winston to pilot a playoff team and this could easily blow up in Sean Payton's face.
Injury is a possibility, as with the other teams. If Winston gets hurt the Saints would be better off signing Rivers and allowing Hill to continue his role rather than making Hill an every-down quarterback.
However, there is also the Carson Wentz possibility of the Saints winning despite Jameis Winston. In this situation, it is more likely that they start hot with some easy opponents and then start to taper down as Winston falls back down to earth.
Regardless, Payton has a great offensive mind and Philip Rivers would likely jump at the chance to play for him and potentially win a Super Bowl.
It would not be the first time that a former Hall of Fame Chargers quarterback joined the Saints.