The Clarets announced the departure of Dyche, who was the longest-serving Premier League manager, on Friday.
Burnley are currently 18th in the table, three points from safety and twelve behind the Magpies who sit in 13th.
They have just seven games left to ensure their Premier League survival and could look towards a former Sunderland and Newcastle manager to do just that.
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That’s because Sam Allardyce (9/4) is the current bookies favourite to take the job. Allardyce hasn’t had a job in management since leaving West Brom at the end of last season when he failed to keep the Baggies in the Premier League.