Members of the Arsenal hierarchy are concerned that key players will not want to commit their futures to the club if Unai Emery remains in charge.
The Spaniard has come under heavy pressure in recent weeks, with Arsenal having won only two of their last 11 Premier League games.
The Gunners salvaged a 2-2 draw against struggling Southampton on Saturday thanks to Alexandre Lacazette's last-gasp strike.
They are already eight points adrift of the top four, however, and face an uphill battle to qualify for next season's edition of the Champions League.
Reports on Monday suggested that Emery will be given three more Premier League games to turn the situation around after head of football Raul Sanllehi and technical director Edu held crisis talks with the under-fire manager at the end of the Southampton game.
But the Daily Mail write that officials at the Emirates Stadium are worried that the team's star players will look to leave the club if the former Sevilla and PSG head coach remains at the helm next season.
Strike duo Pierre-Emerick Aubameyang and Alexandre Lacazette are both stalling on new deals, which has alarmed senior figures inside the club.
Several members of the squad have major reservations about Emery's approach, believing his game plans are too cautious and bemoaning a lack of consistency week to week.
And while Arsenal do not want to be too hasty in pulling the trigger, they may decide to act if it helps the north London outfit secure their star players' long-term futures.
Emery will be looking to relieve some of the pressure when Arsenal take on Eintracht Frankfurt in the Europa League on Thursday.
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