The North London outfit gave rivals Chelsea the green light to sign the England international on Tuesday, but the 24-year-old turned down the Premier League champions in favour of a switch to Anfield.
Before the mainstream media got hold of details that Arsenal have accepted Liverpool's bid, Oxlade-Chamberlain's management company Colossal Sports MGT tweeted an image of Liverpool's club crest with "deal agreed" as the caption. It has since been deleted.
Neville, who played for Manchester United between 1992 and 2011, reacted angrily to the alleged announcement.
The former full-back wrote: "Embarrassing!! Has it been deleted!! Thought so. Clubs not even announced yet."
Oxlade-Chamberlain has spent the last six years at Arsenal following his 2011 switch from Southampton.