He started his career with the Lions more than 20 years ago before moving on to Nottingham Forest, Manchester United and Spurs (twice).
At Old Trafford, he won the Treble and scored one of United's goals in their Champions League Final victory over Bayern Munich in 1999.
Despite injury problems last season, Sheringham, who won 51 caps, scored nine times as Pompey successfully avoided relegation in their first season back in the top flight.
West Ham play the first match of their three-game pre-season tour of Sweden against Second Division side Umea FC in Umea tonight. They also have games against GIF Sundsvall on Thursday and Friska Viljor on Monday.