The 24-year-old has made 27 appearances for Olympiacos this season and has also been on the radar of Napoli.
However, it is Patrick Vieira’s Nice who are closing in on the highly-rated Tsimikas.
The clubs are negotiating the terms of the deal, with €8m plus bonuses the fee under discussion.
Tsimikas will sign a three-year deal with the option of a fourth at the Allianz Riviera.
The Ligue 1 side have secured Europa League football next year and are already active in the transfer market.