The Serie A side have been represented at the meeting by former Spurs sporting director Franco Baldini, according toSky Sport Italia.
Baldini meets Tottenham chairman Daniel Levy in the hope of lowering his asking price of £25 million for the centre-back.
The Belgium international has a clause in his contract that means he can leave for that figure any time up to two weeks before the transfer window shuts on August 8.
Further complications for the Italian club are the high demands Alderweireld’s representatives presented during a meeting with Roma officials on Thursday.
The 30-year-old is in the final year of his contract in north London, but is expected to join his team-mates for their pre-season trip to Asia.