Sky Sports had advertised former Newcastle United head coach McClaren as a guest for this week's Goals on Sunday show.
McClaren hasn't spoken since being sacked by the club in early March.
But the 54-year-old has now been replaced as a guest on the sofa by Allardyce, whose Sunderland side secured their top-flight status on Wednesday night with a 3-0 win over Everton.
That result at the Stadium of Light meant relegation for Newcastle.
After the broadcast on Sunday, Allardyce will travel from Sky's London studios to Hertfordshire, where his team take on Watford in their final game of the season.
Allardyce will be joined on the coach by Burnley manager Sean Dyche, whose side clinched promotion to the Premier League earlier this month.