Fazio has now made a specified number of appearances for Roma to pay £2.8m to keep him on a permanent basis, following his arrival on a season-long loan from Spurs last summer.
The Argentine has become a key man at the Stadio Olimpico and, according to Gazzetta dello Sport, Roma will keep him by paying the agreed fee.
Allied to the £1m loan fee paid to Tottenham to sign Fazio on loan, the defender will cost the Italian giants just £3.8m, which they believe represents superb business.
Roma coach Luciano Spalletti was clear on Fazio's value to the club following Sunday's 1-0 win over Cagliari in Serie A.