Sunderland have already made their first addition of the January transfer window by signing Jan Kirchhoff.
The Black Cats are hoping to bring in a number of players in January, as they look to strengthen their bid for survival.
And Allardyce says that making sure that the players are capable of dealing the pressure, both physically and mentally, at the Stadium of Light is important.
“We have to make sure that they are talented, physically capable and mentally strong,” he said.
“We’ve done a lot of the groundwork. You find out very quickly if the position of the club in the table, or where it is geographically, is going to be a factor.
“You speak to the agent and ask if their player will come to Sunderland and want to fight against relegation. Yes or no? If it’s yes, let’s talk. If it’s no, on to the next one.
“They are the first questions you ask, and you tend to get very quick and simple answers.”
Sunderland made their first signing of the January transfer window by signing Jan Kirchhoff from Bayern Munich yesterday.
Kirchhoff has signed a 18 month deal with the Wearsiders, and is expected to go straight into Allardyce’s side’s defence.
Sunderland are still on the lookout for further additions, with a host of players linked.
Reports in the Chronicle today suggested that Sunderland were interested in Borussia Dortmund striker Ciro Immobile, but a deal for Lorient defender Lamine Kone has fallen through.
Sunderland's next match comes against Arsenal in the FA Cup on Saturday.