Despite public backing, Unai Emery has six games to prove he's still the right man for Arsenal - report
Emery has come under heavy pressure in recent weeks, with Arsenal now eight points adrift of the top four.
Saturday's 2-0 defeat by Leicester means the Gunners have now won just two of their last 10 Premier League games.
Emery has also been criticised for Arsenal's lack of on-field identity, as well as for failing to get a grip on disciplinary issues off the pitch.
It has also been reported that Emery has come under fire from several members of his squad for stripping Granit Xhaka of the captaincy following the Swiss' clash with supporters during a 2-2 draw with Crystal Palace.
However, despite losing the support of many Arsenal fans, the powers that be at the Emirates Stadium delivered a vote of confidence to their manager on Monday.
Head of football Raul Sanllehi and managing director Vinai Venkatesham both retain faith in the former Sevilla boss.
Nevertheless, the Evening Standard report that Emery must oversee a turnaround in Arsenal's next six games if he wants to remain in position.
The Gunners face struggling Southampton after the current international break, before a home clash with Eintracht Frankfurt in the Europa League.
A positive set of results would justify the faith Sanllehi and Venkatesham have placed in the Spaniard.
But a continuation of Arsenal's poor recent form could force the board to act before the transfer window reopens in January.
Emery is under contract until summer 2021, but a break clause in his deal will allow Arsenal to part ways with the 48-year-old at the end of the season.