Just throwing a dart here, but I'll say Tampa? Kyle Trask is a FA this year, and a team interested in Rush is probably a playoff contender that wants a step in and win 1-2 games to keep you afloat type backup which is what Rush is.
Other teams to watch might be New Orleans due to the KM/Nussemeier connection, but I would think they would want to go with someone young and developmental behind Carr. Minnesota could be interested as a vet influence JJ McCarthy backup in what is essentially his rookie year. Detroit could be a sneaky pick too depending on how they view the development of Hendon Hooker. They brought in Bridgewater late last year so I would guess they dont think as high of him now as they did when they drafted him.
The issue for Rush is going to be that the backup QB FA market this year is a pretty decent one. The draft seems to lack a high volume of potential starters, but there are a lot of guys with multiple years of starting experience in college that profile as plug in day 1 backup QB types. There should be a ton of competition for backup jobs this year and Rush is a polarizing guy who has proven he can win games, but also hasnt looked overly impressive doing so.