Sanchez is out of contract in 2018 and talks over a renewal are on hold until the end of the season.
If the Chile international cannot be convinced to extend, former Arsenal star Merson does not think Chelsea's status as a rival club would stop Arsene Wenger from selling, given he would be desperate to avoid losing him for nothing the following year.
He feels the 2012 sale of Robin van Persie to Manchester United when he had one year left on his contract is a sign of what is likely to happen at the end of this season.
"I think Sanchez will leave this summer," Merson said to Sporting Life.
"I don't think Arsenal will finish in the top four and if they don't finish in the top four then I don't see him staying.
"I know the way Arsenal work so there is no way they will let Sanchez leave for nothing if they can get £50m for him in the summer.
"They will have no qualms in selling him to Chelsea. Arsenal will have no choice - if Chelsea are the team that are prepared to pay £50m then Arsenal won't let him see his contract out.
"People say, 'Oh well, they won't sell to Chelsea', but they sold Robin van Persie to Manchester United so they won't be fussed about that.
"I definitely think Sanchez could be a Chelsea player next season. He is a world-class footballer so he would fit in at Chelsea.
"People say he is not the same player but he will get you a lot more goals than Hazard. If they can sign Sanchez for £50m and get £100m for Hazard then I think that is good business."
51 - Arsenal have won the same number of points after 28 games this season as they did in 2015/16, with the same record (W15 D6 L7). Level.— OptaJoe (@OptaJoe) April 2, 2017
Merson believes Arsenal only have themselves to blame for the Sanchez situation, while Mesut Ozil is another key player with just over a year left to run on his deal.
"It is terrible how Arsenal can let a player of that talent [Sanchez] run the years down on his contract," he said.
"There's about eight of the players with contracts running down and I find it extraordinary that they are in this situation.
"Because of everything going on with Arsene Wenger, I think they have just forgotten about the players."