Newcastle, who also sit in the relegation zone, have themselves struggled this season and picked up their first win of the campaign in Sunday's 6-2 drubbing of Norwich.
Allardyce, who is the only man to take charge of both teams, will be hoping the recent trend of results between the sides continues as Sunderland have won their last five games against the Magpies.
"No. I've got to look after the reputation of Sunderland. The pressure's on me, more than it's on Steve. We've won the last five, so I don't want to be the one who doesn't win it," Allardyce told the Sunderland Echo.
"But we'll wait and see on the players; only the players can make everyone smile next week. They just have to carry on what they have done five times before.
"They have been struggling but won the last five games against Newcastle. They don't need me to coach them this week. Let's hope for the same again," he added.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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