The 43-year-old front-man, who won 51 caps for his country, has been asked to participate in the club's FA Vase encounters during 2009/10.
Sheringham, who made more than 200 league appearances for Spurs scoring 98 times, has not played competitively since leaving Colchester United in summer 2008.
However, Beckenham chairman Chris McCarthy remains hopeful of snaring the star's services for the previously little-known Kent League Premier Division club, who reached the fourth round of the FA Vase in 1980/81.
"I'm having talks with Teddy about the situation but these things do take a lot of sorting out," he told the club's website.
"I'm really hopeful that between us we can make the situation become a reality. It's an enormously exciting prospect."
The striker, who began his professional career with Millwall in 1983, was part of the treble-winning Manchester United side in 1999, with Sheringham netting in both the FA Cup and Champions League finals against Newcastle United and Bayern Munich respectively.
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