Manager Darren Ferguson is predicting that Posh could cause an upset should Rovers field an inexperienced side for the match.
"It is a winnable tie," he has said.
"Sam Allardyce played a reserve team in the last round and I would imagine he may do the same again."
Full 4th Round Draw:
Blackburn v Peterborough
Man City v Scunthorpe
Tottenham v Everton
Barnsley v Man United
Chelsea v Bolton
Sunderland v Aston Villa
Arsenal v Liverpool
Portsmouth v Stoke