Shearer has a poor relationship with club owner Mike Ashley after the billionaire put the club up for sale.
Shearer has emerged as a contender for the role to replace Tony Mowbray as West Brom manager.
Mowbray is expected to be named new Celtic manager this week.
A source close to Shearer told News of the World: “The delay is damaging. It has been frustrating for Alan. He will not commit career suicide.”
Two rival consortiums are believed to be interested in buying Newcastle, but a sale is not expected to be done until July.