Martial, who is also a top target for Serie A giants Juventus, "was disappointed at not having the chance to discuss a move to Arsenal in January," per Paul Hirst of The Times (h/t The Sun's Andrew Richardson).
Although Arsenal boss Arsene Wenger asked if Martial might be included in the Sanchez deal, he has now "prioritised other areas to strengthen this summer," according to Olley. Those areas include centre-back, midfield and a new goalkeeper.
Olley noted how Wenger "remains an admirer of Martial having tracked the Frenchman since his Monaco days." Yet the Gunners appear well-enough stocked in attacking areas thanks to the presence of Alexandre Lacazette, Pierre-Emerick Aubameyang and Danny Welbeck.
Arsenal do have ample firepower up top, but there is no doubt Martial could add a lot to any forward line in the Premier League. His pace, technique and versatility would all find a home within Wenger's progressive style of play.
Opportunities aren't likely to be readily available at Old Trafford. The arrival of Sanchez in January and the solid first season in United red enjoyed by Romelu Lukaku have seen Martial overlooked regularly by manager Jose Mourinho in 2018.
It doesn't help Jesse Lingard has accelerated his development on Mourinho's watch. The England international has bagged 13 goals and supplied four assists across all competitions.
Like Martial, Lingard can play on either flank or operate centrally, albeit in a withdrawn role behind the main striker. Being in and out of the starting XI has hindered Martial's performances.
"Martial looked distracted and off the pace at Old Trafford. In 31 minutes, he did not manage a shot, create a scoring chance or even complete a cross. Even more damning, he lost possession 13 times without winning it back once."
He may have his problems in Manchester, but Martial still makes sense as a target for the Gunners. His direct running, physical power and eye for goal would add another threat to a potentially awesome forward line.
He could play wide left, with Mkhitaryan right, Aubameyang through the middle and Mesut Ozil as the chief supplier. Alternatively Aubameyang and Martial could flank Lacazette in what would surely prove a prolific front three.
Wenger's team is built to attack and remains more than capable of scoring goals in bunches, regardless of any issues at the back. Welbeck's contract is up in 2019, while Aubameyang will be 29 in June, so Arsenal could use a younger striker.
Martial is still only 22, yet he is also a proven commodity at this level. He has genuine star potential likely to be unleashed in a more progressive setup.
Arsenal will need a statement signing of sorts after another dismal league campaign, during which fans have started to stay away from the Emirates Stadium in numbers. Landing Martial would be the right kind of statement the Gunners are determined to restore former glories.