The Gunners are reportedly offering both Chelsea and Manchester United the chance to sign Lewis-Skelly this summer, as the North London side cannot offer him the game time he expects next season.
Lewis-Skelly started the Champions League final over Martin Zubimendi, a game which may be his last for the side who are seeking to offload him before the Premier League kicks off in less than two weeks.
The teenager would be competing with Bruno Guimaraes, Declan Rice, Martin Zubimendi, Martin Odegaard and Mikel Merino. At left back he would also go up against Ricardo Calafiori and Piero Hincapie who he would not be able to displace.
Speaking on the news, Dixon believes that a swap deal could be made with United for Marcus Rashford who recently returned from loan at Barcelona where he grabbed 14 goals and 14 assists.
"Would I swap them (Myles Lewis Skelly and Marcus Rashford)? You know what, I probably would," Dixon told BestBettingSites. "And that's nothing against Myles Lewis-Skelly, it's about giving him the freedom to go and expand his game elsewhere.
"With Marcus Rashford, he's a player who needs an arm around his shoulder, and Arteta would be great for him.
“Give him that love, give him the freedom to play on that left side, and yeah, I'd like to see him in an Arsenal shirt. I have my reservations about whether he's consistently a top-class player, but based on what Arsenal have in the squad now, he'd be a good addition."
Lewis-Skelly has been on the books at Arsenal for 11 years and has played 75 times for the first team since breaking through the academy. A move away looks almost certain but a switch for Rashford looks unlikely as the England star reintergrates into the United side.