The Daily Mail says Allardyce stunned West Ham's players by ordering them to attend a 7am team meeting, hours after their 5-1 defeat at Arsenal.
The exception was Diame, who turned up one hour late at the Chadwell Heath training ground.
Diame has a £3.5million release clause in his contract. Allardyce is understood to be angry at his failure to report on time, and the club insisted last night that it would fall under the appropriate disciplinary measures.
West Ham are treating the Diame case sensitively because Arsenal are about to activate the release clause inserted into his contract when he signed from Wigan last summer.
The Hammers were already 5-1 down when Diame, who wants to join Arsenal, came on as a 70th-minute substitute.
Diame later took part in a full training session but West Ham are struggling to hold on to one of their best players.