The conversations are part of the extensive data that judicial investigators in Cremona have been sorting through in a match-fixing inquiry into soccer.
In a July 2007 conversation on Skype between Bracciali and an accountant who was arrested in 2011, Bracciali discusses 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 parlour who was later arrested is heard saying that Starace agreed to sell the final of a tournament in Casablanca.
Pablo Andujar of Spain won the final 6-1, 6-2.
Prosecutor Roberto Di Martino, who is leading the Cremona inquiry, confirmed to The Associated Press the authenticity of the conversations.
Di Martino added that foreign tennis players might also be involved.
"I can't rule that out," Di Martino told the AP. "But I can't say anything more for now."
Bracciali and Starace, neither of whom are officially under investigation, refused to comment after pairing together to win a first-round doubles at the Kremlin Cup in Moscow on Wednesday.
The Italian tennis federation (FIT) said it will request copies of all the documents from Cremona authorities involving tennis players.
"If the inquiry confirms what went on in the intercepted conversations published by the newspapers then we'll be dealing with serious and intolerable offences," FIT president Angelo Binaghi said in a statement.
The Last Bet operation has resulted in more than 100 people placed under investigation in Italy since mid-2011, with suspect soccer matches being looked at by prosecutors in Cremona, Bari and Naples. The inquiry is branching out to other sports.
The 36-year-old Bracciali is a doubles specialist while the 33-year-old Starace is ranked 150th in singles.
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 ranging from six weeks to nine months for betting.
In other cases of match-fixing in tennis, life bans were handed to Daniel Koellerer of Austria in 2011, David Savic of Serbia in 2012, and Andrey Kumantsov of Russia this year.
In July, one man was charged and five others arrested in an Australian police operation against an international tennis match-fixing syndicate.
Andrew Dampf can be followed at www.twitter.com/asdampf