Manager Arsene Wenger held a meeting with Arsenal owner Stan Kroenke on Monday, at which the Frenchman's future was expected to be decided.
The outcome is unclear but the decision rests solely with Wenger and Kroenke and will be relayed to directors at a Tuesday board meeting.
Fresh terms were agreed in principle months ago, but nothing has been signed to extend Wenger's 21-year tenure.
Arsenal are planning to make an announcement on Wednesday.
Although Wenger, 67, also met chief executive Ivan Gazidis on Monday, the time he spent with Kroenke would have been decisive.
The businessman has privately reiterated his support for the manager and his commitment to providing him with the resources he needs to win the Premier League title.
Wenger is acutely aware of the disruption his departure could cause, which is one of the reasons why it is most likely he will extend his reign. However, it is not definitive.
Arsenal are planning to make a statement and release an interview with Wenger on Wednesday, when further internal changes are expected to be outlined.
Those will not be drastic nor impinge on the manager's control over the technical side of the club.
There is no prospect of a director of football being appointed, though a lower-profile role to enhance Arsenal's work in areas such as scouting and contracts is under consideration.
Transfer and contract negotiator Dick Law, whose own deal expires in September, will keep his job for the time being.
Split on the Arsenal board
Wenger's preference has always been to stay, but the determining factor was how he believed the atmosphere around the club would be affected by him doing so.
He has faced unprecedented criticism during a season in which the Gunners finished outside the Premier League's top four for the first time in his reign.
However, they beat Chelsea on Saturday to win the FA Cup, making Wenger the most successful manager - and Arsenal the most successful team - in the competition's history.
Although Kroenke has never wavered in his desire for Wenger to remain in charge, certain board members feel the time has come for the Frenchman to leave.
However, all power lies with the American, so Wenger's main concern is external opposition and the conditions that might create for his players next season.
He has admitted the uncertainty over his position did not help performances or the mood around the club, and that it should have been resolved sooner.
Arsenal lost seven of 12 matches between 31 January and 10 April, including a 10-2 aggregate defeat by Bayern Munich in the Champions League last 16.
They responded by winning nine of their last 10 games, but a fifth-place finish in the league ended their run of 19 consecutive years in the Champions League and means they will instead contest the Europa League next season.