Depends on 1) when a team decides to build around a goalie next or 2) how fast inflation due to rising cap catches up to Price's salary cap range.
My guess is the latter happens first, and within 5 years. A few possibilities:
Bobrosvky @ 7.425m (UFA this year)
Holtby @ 6.1m (UFA 2020)
Vasilevskiy @3.5m (UFA 2020)
Andersen @ 5m (UFA 2021)
Rask @ 7.0m (UFA 2021)
Helleybuyck @ 6.2m (UFA 2024)
Jones @ 5.75m (UFA 2024)
Add John Gibson to this. I'd say his chances of it are decent.
Not sure why Jones is even a possibility. He's too average and dime a dozen. Rule out Jones completely here. There's a better chance Jones gets bought out before his current bullshit deal ends than getting $10 million a year. Maybe if Chiarelli is the Sharks GM by then, Jones will get nearly as much or more than Price is currently making, but if that happens, there's bigger problems with the Sharks than that. A mediocre to average at best goalie at 29 years old making that much money at age 34? No chance.
I don't see Bobrovsky getting Price money this year. Having a down year (by his standards) probably hurts him a bit. He may not even get much more in AAV than he is now if the term is very long.
Holtby is a possibility. Being pretty average his last two years might keep that from happening though.
Vasilevskiy is a real possibility
Rask's best days are behind him. Doubt he makes more per year on his next deal than he's making on this one. He'll be 34 years old when that contract starts.
I'd only say it's a possibility for Hellebuyck because it's 5 years away and salaries could be through the roof by then, but probably not.