The Hammers scored just 40 goals during the last campaign as they secured a 13th-place finish in the Premier League table.
Allardyce is hopeful that former England and Manchester United striker Sheringham will be able to pass his expertise on to the forwards at Upton Park.
"Teddy is someone I have known for many, many years," Allardyce told Sky Sports News.
"He's had a long spell out of football since he retired, after a fantastic career that lasted well into his forties. Now he's hungry and ready to give something back.
"We hope that he can bring in a new phase, a couple of different ideas, and specifically work with the front men to score a few more goals."
West Ham get their Premier League campaign underway at home to Tottenham Hotspur on August 16.