"Probably, it'll have to be from abroad, by the looks of what's about and available in this country," Allardyce told British media.
"I think it would be very difficult to secure a player from any club in the Premier League because I don't think they'd want to let anybody go," he added.
"So, for me, it looks like it might be from abroad, and then see where we go from there.
"We've got to get back to being a resilient defensive unit... but the backline and the goalkeeper have to be the ones that ultimately secure those clean sheets, so a defender's my first priority, a central defender."
Allardyce said his side were destined to be relegated if they did not regain their killer instinct in front of goal.
"At the top end, we're not looking very clinical with the chances we had," the former West Ham United manager said.
"We're making far too many mistakes at the minute."
Allardyce is likely to be without preferred centre-back pairing of Younes Kaboul, who is out for two months with a hamstring injury, and skipper John O'Shea for Wednesday's game against Liverpool.
"Our defensive problems have re-arisen with Younes being injured for a period of time and it looks like John O'Shea has picked up a calf injury," Allardyce told reporters on Monday.
"It's not too serious, it's not as serious as Younes, but he might miss Liverpool. I am erring on the cautious side.
"We've still got Wes (Brown), but obviously Wes's problem is how few games he has played. But ... he has got a huge amount of experience that we hope he can use."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Ed Osmond)
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