Mark Hughes has been expected to come back with a fourth offer for the forward, but with Matt Derbyshire going to Greece, Roque is needed all the more.
"There is not the opportunity now to get the quality of striker we need to allow us to even consider letting Roque Santa Cruz move to Manchester City," said Allardyce.
"So for me, he stays, although I can't put it to bed completely until the deadline has passed.
"It's impossible, from any manager's point of view, to see what happens between now and then.
"But I certainly wish it was the 3rd of February tomorrow."