The sad reality is that it probably won't be "cheap".. Although the situation is not exactly the same, just 3 years ago Calgary gave the Canadiens a 1st-round pick to take Sean Monahan and his final contract year.
Joshua Roy could be sacrificed by the Canadiens in the Price contract trade
Most observers expect that the Canadiens will have to pay at least a 2nd-round pick to convince a team to take Price's contract, but it's not impossible that Kent Hughes instead decides to offer a young player with some potential to "close" the deal.
That's where the name Joshua Roy comes into play.
We know the Blackhawks are one of the teams with the necessary cap space to acquire Price's contract. We also know that Connor Bedard and Joshua Roy, who still has a lot of potential, got along like best friends when they were paired together at the World Junior Championships.
We can also bet that Kyle Dubas, another GM who could afford to pick up Carey Price's contract, would gladly take a young player like Joshua Roy to inject youth into his extremely aging team.