With the new Premier League season now just six weeks away, Allardyce is growing increasingly anxious in his desire to fill the obvious void in his squad.
Allardyce said: "I have been in touch with our head of player recruitment Martyn Glover and Neil McDonald while taking a break to see what the situation is regarding the one key player we are looking for.
"Unfortunately that hasn't managed to materialise at the moment.
"We are at a situation where we have to commit to someone otherwise what will happen is we will end up with nobody. Or we will end up with someone that is not good enough out of desperation.
"That is the problem we have got. Anyone who has had a decent World Cup will end up being far, far too expensive for us.
"That is the situation you are going to come to with everybody who plays in the World Cup. If a striker from a more obscure country plays well and you ring up about him they will start at £8million and work upwards.
"That is our of our budget range."