End of an epic: Andrei Arshavin is set to learn whether he will be allowed to join Arsenal
The Russians say the£12million offer - rising to about£15m with add-ons - must rise, but they are ready to back down on their public valuation of£20m.
The board were convened after their general director Maxim Mitrofanov, who is sanctioned to hold talks with Arsenal, revealed he had reached stalemate in the negotiations. Zenit chairman Alexander Dukov will decide how low they are prepared to go.
Mitrofanov said: 'It seems that we are more interested that Arsenal in negotiating: Zenit meets the player half way, shows the initiative, offers various options, but the Englishmen hold their ground.
'But, in any case, the decision concerning sale or not of Arshavin can be accepted on Friday or Saturday.
'Arshavin will not be sold for the sum of£12million in any event - representatives of Arsenal have known this for the past month.'
Both clubs are keen to settle the deal one way or the other. Zenit have set a deadline of Sunday, while Arsenal boss Arsene Wenger wants to know by Monday whether he will have to look elsewhere for targets to improve his squad.
Zenit took the unusual step last autumn of allowing the Russia forward's agent to negotiate directly with clubs and it is thought that he has virtually agreed terms already with Arsenal.
Euro star: Arshavin impressed for Russia at the European Championship last summer
Although clubs in Spain and Italy were interested, Arsenal's bid is the only one on the table. The Russians must decide whether to cash in now or risk losing him on the cheap in November at the end of their next domestic season.
He would then be eligible under FIFA rules to buy out his contract, perhaps for as little as£2.5m.
Wenger remains relaxed about the pursuit and he intends to keep his own counsel until the deal is concluded one way or another.
'It is in the newspapers, but not from our side. We are quiet and we know what we want to do,' the French boss told Arsenal TV Online. 'We will keep that as quiet as possible and for as long as we can.'
Calm: Arsenal manager Arsene Wenger
The Gunners boss feels should the transfer not come off, then such public statements of the ins and outs of the negotiations could result in a backlash from the fans.
'It is difficult because I believe when it does not work, it can turn against them or against us,' said Wenger.
'You have to accept that in the transfer market, sometimes you go for a player and that sometimes it happens, and sometimes it doesn't happen.
'But I am very happy with the squad I have and will only add someone who can give us something special.'