Sheringham, available on a free-transfer following his release from Tottenham at the end of last season, is expected to decide on his future early next week when he reurns from holidaying in The Algarve.
Charlton, who signed Pompey target Matt Holland recently, are also rumoured to be on a short-list of five teams that Sheringham has been offered a deal by.
However, Redknapp told The News: "I'm confident Teddy will sign.
"I've got on well with him when I've met him, and I've just got a feeling he will come and play for us."