The Bianconeri were long linked with the former Lazio wing-back and reports coming out of both England and Italy suggest they’re stepping up their attempts.
It is claimed Juve have sent a formal €12m proposal (£10.5m) to Manchester City for the Serbian international.
Kolarov has publicly complained about the lack of playing time at Eastlands and would welcome a return to Serie A.
Inter have also shown an interest in his situation, but Juve can promise Champions League football.
Alessandro Matri is considering a transfer to Napoli after Juventus reportedly accepted a €12m (£10.3m) offer.The striker is known to be on the market after the arrival of Carlos Tevez and Fernando Llorente.
He had been linked with Milan, Everton and Liverpool, but SportMediaset claim Napoli are now in pole position.
Juve were originally hoping to earn €15m (£12.9m) from his sale, though it is reported they have accepted a €12m (£10.3m) bid from the Partenopei.
According to the reports, Matri has taken a couple of days to consider the transfer.
Napoli are seeking another striker after signing Gonzalo Higuain, but ran into difficulties for Porto’s Jackson Martinez and Palermo forward Abel Hernandez.
It’s reported Wolfsburg are prepared to pay €20m (£17.2m) for Roma and Italy forward Pablo Daniel Osvaldo.
The striker is on the transfer list after a series of problems with management, club chiefs and fans.
He had been linked with Southampton, Tottenham, Arsenal, Manchester United, Valencia and Napoli among others.
According to Sky Sport Italia, Bundesliga side Wolfsburg have now come forward with a €20m bid to sign Osvaldo.
They are also offering a contract worth €2.8m (£2.4m) per season.
Osvaldo has earned a recall to the Italy side for the friendly against Argentina on August 14, as he was dropped for the Confederations Cup after insulting then-Roma Coach Aurelio Andreazzoli.
Spanish newspaper Marca claims Carlo Ancelotti has made an enquiry with Milan for ‘Little Maldini’ Mattia De Sciglio.
The versatile 20-year-old can play as a right-back or left-back, plus in wide midfield roles when needed, and is already a senior Italy regular.
Known as the ‘new Paolo Maldini,’ De Sciglio grew up in the Milan youth academy.
It is suggested the Rossoneri could be prepared to release him for as little as €12m (£10.3m) and his current contract expires in June 2016.