The defender is only tied to the club until June 2023 and in theory from next month could start negotiations for a free transfer in the summer.
Paris Saint-Germain already saw bids worth over €60m rejected by Inter directors, who were confident they had already agreed an extension.
However, the interest from PSG, Tottenham Hotspur, Chelsea and others inevitably raised his wage demands and forced the club to renegotiate.
According to Sky Sport Italia, a response has not yet arrived from Skriniar or his agent to the latest proposal put forward by Inter.
It is reported the wages will reach €6m per season net, the maximum under their current salary cap, with up to another €1m in performance-related bonuses.
This is still a long way behind the Paris Saint-Germain proposal that was believed to be worth €10m per season.