Sunderland have until 11pm on Monday to boost their arsenal for the remainder of the relegation battle, with the Black Cats making three modest acquisitions to the squad, Jan Kirchhoff, Dame N’Doye and Steve Harper, so far this month.
Allardyce wants another defender and attacker before the deadline, and spent the weekend scouting a potential target.
But the Sunderland boss will also be on the look-out for additions who would seem unlikely to join a side lingering second bottom of the table; four points adrift of the safety mark.
Allardyce pulled off that feat regularly at former club Bolton, citing the example of World Cup winner Youri Djorkaeff, who joined the Trotters in the winter of 2002, when they were battling to remain in the Premier League.
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He said: “You’ve got to find out if that quality of player wants to come and join you, and ask the question.
“Sometimes, the circumstances will allow you to sign them, especially with the European Championships coming up this summer.
“For instance, Youri Djorkaeff came to me because he needed to play first-team football, so he could play for France in the World Cup that year.
“Otherwise he wouldn’t have even bothered with Bolton Wanderers.
“In fact, he wouldn’t have even known where it was.
“But because it was a necessity for him to play first-team football, we were the only club that could give him a shot and he saved us. And then he stayed for three more years because he liked it that much.
“Sometimes, these things can all fall into place.
“I never thought at the start of that window that I’d be able to get a Youri Djorkaeff, but through the agent and trying, you can hopefully pull one off.”
Allardyce and Sunderland chief scout Steve Houston have been personally checking on a variety of targets throughout the window.
But Allardyce admits that to land those shock buys such as Djorkaeff, then agents play a big part in offering the services of their clients.
“They come to you via agents today, so the agents find out first,” added Allardyce.
“Whatever people call agents, they’re the way of the world today and sometimes they find you a player that you can’t normally find through your own systems.”