The Times' back page headline on Thursday read: "Arsenal plunge into chaos as Dein departure splits the board", while The Sun predicted: "Club face 650 million pounds hostile U.S. bid."
The same paper also said the futures of manager Arsene Wenger and striker Thierry Henry were in doubt.
Dein, who brought Wenger to Arsenal in 1996, quit because of "irreconcilable differences" with fellow board members.
The Times, noting that 63-year-old Dein holds 14.5 percent of the club's shares, said there was an "intriguing possibility" that he could sell to American businessman Stan Kroenke, who recently bought an 11 percent share.
That could force a hostile takeover bid, said the paper.
The Sun's business editor said Dein's departure almost certainly means that in financial jargon Arsenal are "in play."
Although Chairman Peter Hill-Wood and the other board members own 45.45 percent of the shares and are committed to retaining them, that still leaves over 50 percent that could fall to Kroenke, who has various sporting franchises in the U.S.
The Sun says that if Kroenke bought Dein's share he would not be far short of the 30 percent needed to trigger an automatic takeover bid under stock market rules.
The Star notes that Henry is represented by Dein's son Darren and has close ties with the former vice-chairman.
Arsenal's big rivals Manchester United and Liverpool are owned by Americans. Champions Chelsea are owned by Russian billionaire Roman Abramovich.
