Sheringham is currently an attacking coach at Upton Park and any deal with Stevenage would see the 49-year-old former Tottenham and Manchester United striker take his first job in management.
Current Stevenage manager Graham Westley is out of contract this summer.
Sheringham retired from competitive football at the end of the 2007/08 season with Colchester at the age of 42.
He scored 98 goals in two spells with Spurs, between which he won three Premier League titles, an FA Cup and the Champions League with Manchester United.
He was capped 51 times by England, scoring 11 goals.