Both Sunderland and Norwich City face the two sides in their final two games.
Tuesday evening saw Newcastle United face Manchester City and take away a vital point that saw the Magpies move within two points of safety.
The result blew open the relegation battle this season with it looking likely to go right down to the wire as a result.
Newcastle will be hoping that at some point their rivals, Sunderland and Norwich, slip up to give them a chance of making it into 17th place in the table.
Interestingly both of those sides take on both Watford and Everton in their final two games, and Quinn believes they could determine who goes down.
“Let’s say the Crystal Palace and Aston Villa games go well [for Newcastle],” he told Sky Sports.
“If they get themselves right back into it, I think Everton and Watford will almost determine who goes down. If you look at those crossover games, they’re huge.”
The games against Watford and Everton could certainly prove crucial given both sides' seasons are pretty much concluded.
Neither are in threat of relegation, while significant movement in the league is unlikely at this late stage.
Indeed, for the Blues in particular much will likely rest on how they fare in the FA Cup, with them likely to be fully focused on the cup final should they progress past Manchester United.