Sky Sports sources understand Celtic have rejected a bid in excess of £6million from Rubin Kazan for South Korea international Ki Sung-yueng.
The 23-year-old has impressed at Parkhead since joining Celtic from FC Seoul during the January transfer window in 2010 and he helped the club win the SPL title last season.
He has made 85 appearances for the Bhoys, although he missed the run-in to the last campaign due to a hamstring injury.
Ki's form during his time with Neil Lennon's side has often seen him linked with other clubs, and Tottenham Hotspur were mooted as admirers last month.
However, Ki responded to those rumours at the time by insisting he was not looking for a transfer after previously suggesting he would be prepared to discuss a new contract in the summer.
Russian side Rubin Kazan, though, appear to be trying to test Celtic's resolve, with the Bhoys having already turned down an opening offer.
It is understood that Celtic are expecting Rubin to make an improved bid for Ki, while there remains interest from the English Premier League.
The ongoing speculation regarding Ki's future at Parkhead comes at a time when fellow midfielder Victor Wanyama is also being targeted by other clubs.