Owners David Sullivan and David Gold have been trying to bolster the Hammers’ firepower since taking over the club last week and have made a written offer for McCarthy.
The South African is keen to leave Ewood Park for Upton Park after falling out of favour with Allardyce and has refused to report for training until his future is resolved.
But Allardyce said: “We are very disappointed with Benni’s non-appearance for training and will deal with it separately should he remain here after the transfer window has closed.
“We have said all along that we will listen to offers, but only agree to sell if both the commercial and football reasons satisfy Blackburn Rovers. That situation remains unchanged.”
McCarthy, 32, has only started nine games this season and is keen to play in order to safeguard his place in his national team, who will host this summer’s World Cup.
West Ham, who have also been linked with Manchester City’s Benjani Mwaruwari, welcome striker Carlton Cole back for tonight’s visit of survival rivals Portsmouth.