However, the player has not impressed the Rovers boss by failing to turn up for his last two training sessions.
"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," said the Rovers boss.
"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."
Although Allardyce will have no qualms about off-loading McCarthy, he will not do so unless he can find an adequate replacement.
However, the player's refusal to attend training means his chances of having a future at Ewood Park are slim.
West Ham are in the market for a big-name striker having gone public with their interest in former Manchester United striker Ruud van Nistelrooy.
New co-owner David Sullivan said the debt-ridden club were prepared to pay the Real Madrid forward £100,000-a-week but the Dutchman snubbed them for German side Hamburg.
Portsmouth v West Ham To Win Both Halves: West Ham 10/1
Source: Team Talk
Source: Team Talk