According to SportItalia, the Serie A club is prepared to raise its offer to €8m – approximately £6.9m.
Sky Sport Italia maintain the basics of a deal have been settled, with details to be completed next week.
Negotiations continue and Roma would be willing to include Pablo Daniel Osvaldo as part of an exchange deal.
Fiorentina winger Juan Manuel Vargas has been told he can leave, as he doesn’t fit into Vincenzo Montella’s plans.
The Peruvian international spent last season on loan at Genoa, but has been with the Viola since 2008.
“When he came back from the loan spell at Genoa, we were told that he was on the market because he doesn’t fit into Vincenzo Montella’s plans,” agent Jorge Cyszterpiller told Izvestia.
“At the moment we are not negotiating with any specific clubs, but it will not be difficult to find him a new contract.”
Vargas has so far been linked with Rubin Kazan and Eintracht Frankfurt.
The 29-year-old managed 20 Serie A appearances for Genoa last term. He has been in Serie A since joining Catania in August 2006 from Club Atletico Colon.
Inter are reportedly lining up an offer for Bologna creative midfielder Saphir Taider.
The French-Algerian 21-year-old impressed at the Stadio Dall’Ara last season, scoring three goals in 34 Serie A matches, plus two in one Coppa Italia appearance.
According to Sky Sport Italia, Inter have prepared a proposal to sign Taider this summer.
He is valued at approximately €5m.
Taider had been co-owned by Juventus from January to June 2012, but Bologna bought back the other 50 per cent of the contract.
He has French, Algerian and Tunisian citizenship, but has opted to play his international football for Algeria.
Coach Rafa Benitez is eager to be reunited with some of the key players from his Anfield experience.
Reina passed a medical this week and will join on a one-season loan, while today The Mirror claims Skrtel is on his way out of Liverpool too.
Benitez is building a strong squad at the San Paolo with players such as Gonzalo Higuain, Jose Maria Callejon, Raul Albiol and Dries Mertens.
Meanwhile, there are rumours that Napoli’s third choice jersey for this season will have a camouflage print.
Napoli could make a move for Real Madrid full-back Fabio Coentrao, according to reports in the Italian Press.
Il Mattino have claimed this afternoon that the Serie A side are tracking the progress of the Portuguese defender as a potential replacement for Juan Zuniga.
The Colombia international has been linked with a move to Juventus this summer, and Rafael Benitez’s men see the 25-year-old as his ready-made successor.
Coentrao has endured an inconsistent career at Santiago Bernabeu since he arrived from Benfica in 2011.
He could be available for a fee of around €18m.
Napoli have already captured Gonzalo Higuain, Raul Albiol and Jose Callejon from Real Madrid this summer.
The news comes on the same day as Italian papers suggest a deal is close to sign Gervinho from Arsenal for €8m.
Borriello returned to Roma this summer after a loan spell at Genoa, who were unable to agree terms for a permanent move.
It is reported that negotiations could resume for an exchange between Borriello and Genoa-owned Alberto Gilardino.
There are also suggestions of interest from Malaga, though Borriello has reportedly turned down a move to Tottenham.
As for Destro, he joined the Giallorossi from Siena last summer, but struggled to make an impact amid injuries.
The 22-year-old scored six goals in 21 Serie A games last season.