The Ligue 1 side are believed to be willing to pay a transfer fee in the region of €50 million (£40m) for the centre-back, while offering the player a contract worth close to €1m (£800,000) per month.
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Nevertheless, Milan are still undecided as to whether they want to let go of their prized asset, and his representative feels the Brazil international should be rewarded with a pay rise if the Rossoneri veto a move.
"We are waiting for Milan to get in touch. The negotiations from the past few days have made it very clear that they see Thiago as their most important player," Tonietto stated to La Gazzetta dello Sport.
"We're waiting for [Silvio] Berlusconi to make a decision on his future. If they don't want to sell, then I'm confident that they will recognise his value to the club, and make an effort to give him a new and improved deal."
The centre-back's current contract runs until the summer of 2016.