Southampton have won just one game from their opening nine.
To make matters worse the south coast outfit lost 3-0 at Elland Road on Tuesday evening.
Chairman Nicola Cortese has become anxious in recent weeks as the club show little sign of turning around their fortunes, despite significant investment over the summer.
Alan Shearer was a product of Southampton’s youth academy and is highly respected by the club’s fans.
He made over 100 first-team appearances in the red and white shirt before moving to Blackburn 1992.
Although he doesn’t have the finest of managerial records, having been relegated with Newcastle in 2009, the Geordie is seen as a high profile candidate by the board who may be tempted to put their trust in an inexperienced yet respected footballing figure.