The Rovers boss has identified a couple of possible targets and is expected to keep making enquiries over the next few days.
Allardyce told the Lancashire Telegraph: "It is like everything else. You have got to try and move forward even though it might not be the right time for the football club financially.
"It is the right time for the football club from a football perspective.
"You have to trust that we will make the budget right at the end of the transfer window by shifting around the player we need to shift if that player becomes available.
"It is taking the gamble and then if it is above what you wanted to pay then you take the responsibility as a manager to put that right.
"As a manager I have never not put it right, if you look at my record at every club I have been at."