The player’s performances for club and country have attracted attention of the Russian side, who are eager to sign the Swede before the winter transfer window closes on 27th February.
With contracts of both Oleg Kuzmin and Vitaly Kaleshin due to expire at the end of the season, boss Kurban Berdyev is desperate to sign a new right-sided defender.
Rubin are prepared to offer around €1.5 million for the 26-year-old player, although there is every chance Celtic will demand more money.
Mikael Lustig arrived at Celtic on a free transfer from Rosenborg in January 2012 and quickly established himself as a first team regular at Parkhead.
He has made a total of 20 SPL appearances for the Bhoys and scored 2 goals. Lustig is also considered a first team regular in the national team and has started three 2014 World Cup qualifiers.