The Rovers chief had previously stated he would not bring in a new striker unless one moved out, and McCarthy's imminent exit will create the required space in his squad.
Allardyce is believed to have been in touch with City regarding a deal for Benjani, who has been heavily linked with a move away from Eastlands.
West Ham ended an interest in the Zimbabwean, while Sunderland boss Steve Bruce confirmed he was keen on a deal prior to the weekend.
However, reports suggest that the Black Cats have been unable to agree personal terms with Benjani and that may now let in Blackburn.
Another option for Allardyce is understood to be Dindane, who has spent the first half of the season on loan at Portsmouth.
A switch to Birmingham City fell through over the weekend after Blues boss Alex McLeish revealed the club had been unable to agree a deal with Dindane's permanent side Lens.
Reports now suggest Blackburn are considering a move for the Ivory Coast international after he netted five goals in 14 appearances for Pompey.
Stoke 6/5, Blackburn 9/4, Draw 12/5
Source: Team Talk
Source: Team Talk