Andre Villas-Boas's side have been linked with the Portuguese international on a number of occasions this summer but were put off by his asking price.
However, the Daily Star has suggested that Spurs have returned with a fresh bid following the sale of Luka Modric to Real Madrid earlier this week.
Villas-Boas worked with Moutinho at Porto before moving to England and the 25-year-old is seen as a perfect replacement for Modric.
Porto are believed to have informed Spurs that they will not accept a bid less than £24m, with the London club facing a race against time to complete the deal before the transfer deadline on Friday.
Moussa Dembele completed his move to White Hart Lane from Fulham on Wednesday.