The 23-year-old from Montenegro wants to leave the Russian Premier League club, just a year after joining them from IFK Norrkoping in Sweden.
Rubin Kazan have admitted defeat in trying to keep the player and are in desperate need of funds as they battle a financial shortfall.
They paid almost £6million for Haksabanovic but due to their situation, they are prepared to do a cut-price deal.
This has alerted Celtic, who have been monitoring Haskabanovic for some time, but also other clubs in Europe, including Djurgarden, where he spent time on loan earlier this year.
Celtic do have the financial power and lure of group-stage Champions League football on offer, but they will face a tug of war for his services, although the Scottish Sun is reporting that Haksabanovic may undergo a medical with Celtic within the next 24 hours in London.
Rubin Kazan chief Rustem Saimanov said: “Of course, they [Haksabanovic and his team-mate Oliver Abildgaard] both want to leave. We are in talks with them. But we aren’t letting them go for nothing because we want some money for them.
“Our situation is extremely worrying. Our budget has halved. I regard myself as being in a crisis management role.
“Our players all arrive for free now and no club has given us a single penny for transfers. We have been robbed by FIFA and UEFA.
“Everyone says that we have a big budget, but we also have big obligations. All this eats up money.
“Then we have obligations on loans that we don’t want, but you need to repay. We thought we could sell our best players for money which we didn’t get, the TV rights are down too. We budgeted for all this and got nothing.”