With David having the option of moving to Leicester or Sunderland, Peter acknowledges the contribution the former Wimbledon man made last season.
"David has been excellent and we have had no problem with him whatsoever but everyone understands you have to chop and change sometimes to bring a freshness to it," he says.
Sheringham's vast experience in the game is a factor that Grant feels will be a huge bonus to his team-mates.
"There is no doubt that with the experience Teddy has got he will do well; people talk about legs in the game but his legs were always in his brain, really, and I think that is the thing maybe we lacked last year - a football brain when maybe at times you are under a bit of pressure.
"Sometimes you have to kill a game and you need that all round awareness about the game situation - and Teddy has got that in abundance, there is no doubt about that.
"He will be a fantastic asset and players will want to play with him to show how good they are as well - so it will benefit everyone.
"Teddy has won everything there is in the club game; he has played at international level, World Cups, European Championships, and he will be wanting to show he still has something to prove, not just to other people but to himself because he wants to keep playing - and everyone knows he is a fit man."
* A West Ham XI will play Thurrock on Monday, 2nd August.