Let's have 'em all duke it out for the LW spot, mainly Perisic and Martial.
First, sign Perisic till officially confirmed. Then, all of our attackers can train well and perform in games impressively, to impress Mourinho enough to be given games, the Boss does reward players with games for efforts.
Mind that, one player won't play all games throughout the season, there will be rotations, off forms, injuries, suspensions, personal reasons to warrant absence, and tactical reasons, Mourinho will change accordingly.
Also, once Perisic arrives, he'll have to adapt to Jose system and the tougher physical EPL, so the other players may have higher chance to stamp that position as their own before then.
We're aiming to win the EPL and seriously challenges all competitions next season, safer to bet it on an experienced player who have the football qualities and traits that can slot into the team easily and its system giving it its necessary balance, Ivan Perisic, well in theory anyway.
Martial will play games, continue to improve (his workrate does improve under Mourinho) and contribute with goals and assists (impressive stats last seasons despite the inconsistencies and playing lesser games), he's that good and it'll be weird if Mourinho won't use that talent and nurture it.