A move for Stoke's James Beattie is being lined up while Rovers have also looked at Stuttgart's gifted Turkish midfielder Yildiray Basturk. A fee believed to be for £2.25million has been agreed for McCarthy, 32, who stayed away from training this week in an attempt to force through a transfer.
Allardyce said: "We will now look to secure a replacement - we have been inundated with offers of players who are available."
Asked if he was interested in Beattie and Basturk, Allardyce hinted at a possible move, saying: "If those players are available we may start negotiations, but the first thing would be to contact the club."
Blackburn were also linked with Eidur Gudjohnsen, who is now at Monaco, but it is understood that is unlikely to happen.
Meanwhile, Allardyce condemned McCarthy as "unprofessional" and said his conduct is symptomatic of selfishness and disloyalty shown by many players.
Allardyce said: "What he's done is unprofessional. It shows you that the only loyalty a player has got is to himself.
"This is what we deal with today in football, there's not such a thing as loyalty as there used to be in the older days when I was a player.
"It's a selfish attitude they have and that's not just about Benni, that's all players today. If they want something they do anything to try and get it."
Source: PA
Source: PA