Sheringham is a free agent after being released by West Ham, and the 41-year-old is wanted by Eagles boss Peter Taylor.
If he does move to Selhurst Park he will be a team-mate of his son, 19-year-old Charlie.
"I admire him, but if someone does not move from here, then it makes it difficult for me to bring people in," Taylor told the Wimbledon Guardian.
"Teddy looks after himself, is fit, a good professional and can still do a job."