Able to play at left-back or in the heart of defence, Givet's versatility gives Allardyce options in a small squad.
However, Allardyce admits he will need to bring more players in ahead of next season, but realises the club has to balance its books.
Rovers earned £21m from the combined sales of Matt Derbyshire and Roque Santa Cruz but a portion of that will go back into central funds to cover losses.
"Some of the money that has been created has gone to the bank and what money is left will come in for new players," added Allardyce.
"You don't need to be a football manager to know what we need first and that is a striker.
"But we do need to strengthen in other areas too, including the young professionals - 21 players have left since I've been here including Aaron Mokoena, Danny Simpson, Carlos Villanueva, Tugay and Roque Santa Cruz."
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