"However, we have made the decision that, as part of our longer-term plan, we will be appointing a new manager this summer and will be commencing this process immediately".
Ahead of the meeting, Allardyce has hit out at a lack of "decency" after Everton pushed ahead with boardroom changes by appointing Professor Denise Barrett-Baxendale to replace Robert Elstone as CEO with Dr Keith Harris becoming deputy chairman without his knowledge.
But the style of play under the 63-year-old has not been met with universal appeal among Everton fans.
Allardyce was sacked from his job as Everton manager on Wednesday morning and the club are expected to bring in former Watford boss Marco Silva to replace him in the coming days.
He added, "generally there's no smoke without fire".
"We've seen how we got in wrong last time, with the timing of Koeman's sacking and the money that was spent on signings".
Parents of 2 Parkland Victims Running for School Board
Alhadeff is running for a seat in Broward County School District 4 , while Petty is running in Broward County School District 8 . Alhadeff and Petty are being endorsed by a group of Parkland parents called Concerned Citizens of Broward County.
The club apologised to Allardyce in April after a survey was sent to fans asking them to rank their manager's performance on a scale of zero to 10.
Allardyce, whose previous clubs include Bolton, Newcastle, Sunderland and Crystal Palace, landed his dream job with England in 2016 but that turned sour after only one match, with Allardyce stepping down following a newspaper sting.
The Liverpool Echo says that former Watford boss Silva is the favourite to become the next Everton manager.
Whoever is appointed, Stubbs says they face a huge summer as they look to amend the mistakes Everton made in previous transfer windows, having had little to show for the nearly £300million spent since Farhad Moshiri's takeover.
"I've done all that I can, the backroom staff have done all that they can, and the players have done all that they can".
A change in manager could also affect Wayne Rooney's future at the club.
England's all-time top scorer had reportedly agreed terms on a £12.5 million move to DC United in Major League Soccer last week.