The move looked doomed eariler this week when Anderton missed a deadline set by Pompey chairman Milan Mandaric.
However, Spurs manager Hoddle today told the London Evening Standard he was optimistic that the free transfer move would still go ahead.
Hoddle stated: 'I can't say for sure, because it is far from clear, but it might happen. It might be done and dusted today'.
Such a move would make Anderton the highest paid player in Portsmouth's history.
Anderton initially signed for Portsmouth as a trainee in 1990 and made 77 apperances before signing for the North London side for £1.75 million in the summer of 1992. He went on to become an England regular under Terry Venables and Glenn Hoddle, but injuries have blighted his career since.