Bracciali and occasional doubles partner Starace are the focus of an inquiry using intercepted phone and Internet conversations. The probe is being led by judicial investigators in Cremona who are also dealing with a match-fixing inquiry into soccer.
In a July 2007 conversation between Bracciali and an accountant who was arrested in 2011, Bracciali allegedly discussed arranging a match in Newport, Rhode Island, against American player Scoville Jenkins.
Jenkins won 6-2, 6-1.
In 2011, an owner of a betting parlor who was later arrested, is allegedly heard saying Starace agreed to sell the final of a tournament in Casablanca.
Pablo Andujar of Spain won the final 6-1, 6-2.
The federation says there is reason to believe that the players may have been involved in "illicit behavior."
Bracciali is ranked 72nd in doubles. With partner Jesse Huta Galung of the Netherlands, he lost in the first round of the Australian Open last month.
The 170th-ranked Starace has not played an ATP Tour singles match since September.
Cremona prosecutor Roberto Di Martino told The Associated Press in November that Bracciali partially admitted to fixing during a hearing with investigators.
Starace maintains he did nothing wrong.
Bracciali and Starace were already two of five Italians -- along with Alessio Di Mauro, Giorgio Galimberti and Federico Luzzi -- who were given suspensions in 2007-08 by the ATP Tour ranging from six weeks to nine months for betting.
Also last year, one man was charged and five others arrested in an Australian police operation against an international tennis match-fixing syndicate.