Reports in Italy this week clamed Lazio have placed a €150m (£130m) valuation for Milinkovic-Savic, a rumoured target for Manchester United and Real Madrid, but Tare insists the club not prepared to set a formal price tag for the 23-year-old.
The Serbian international has also been linked with Barcelona, Juventus, Liverpool and Paris Saint-Germain and Tare claims that Lazio actually received offers around the €90m (£79m) last summer.
“I don’t know how much he could be worth and I don’t even want to think about it,” Tare is quoted as saying by Football Italia.
“It’s certainly a figure well over €80-90m. Sergej is very important to us and has not yet reached his peak. There are always more players who can be found and developed,” he added.
“I want it to be clear, Lazio have never set a price-tag or asked anything for Milinkovic. We received offers more or less on that level last summer, but they were not taken into consideration.
“Right now there is interest, but nothing concrete. I’ve never spoken to Real Madrid about him, they never approached us.”
Dutch defender De Vrij will leave Lazio as a free agent at the end of the season after failing to agree a contract extension. He had been heavily linked with Liverpool prior to the world record capture of international colleague Virgil van Dijk at Anfield, and is set to join Inter instead.
“I hope that De Vrij can give his best for Lazio to the end, as he has done so far. Let’s just say there’s a very good possibility he could go to Inter,” Tare said.
The 26-year-old centre-back initially joined Lazio from Feyenoord in 2014 after impressing for the Netherlands at the last World Cup.