The Russian giants are prepared to offer around €8 million for the highly rated defender as they look to add some much needed steel to the back line.
Rubin have been keeping close tabs on the Croatia international for a while, and they believe this is the right time to step up their interest.
Namely, the player has been heavily criticized for his poor defensive showings of late and was left out of the starting line-up for the last two league fixtures.
The Russians are hoping to take advantage of the situation and submit a lucrative proposal to both the player and the club.
Dejan Lovren, 23, could be interested in leaving Stade Gerland after publicly admitting he was disappointed by the treatment he had been receiving from Lyon fans.