"I'm happy at Tottenham, but if I came back to Pompey I wouldn't be too upset," said the 31-year-old former England international.
Harry Redknapp has already taken Tim Sherwood from the North London club as well as securing the services of Teddy Sheringham, who was released by Spurs at the end of last season, and a move for Anderton is not out of the question.
"Harry Redknapp likes Anderton. He could be the sort of special player we bring in," said Pompey chairman Milan Mandaric.