Their hopes of landing the Shakhtar Donetsk ace hit a stumbling block last week as it emerged there could be third-party ownership involved.
And their chances have been hit further with Champions League runners-up Borussia Dortmund entering the race for the Armenian midfielder, 24, in the last few days.
The club's chief executive Sergei Palkin said: "I don't know where Mkhitaryan is now, solely his agent knows this.
"Borussia offered £19.5m. I contacted Mkhitaryan's agent on Tuesday. I wrote to him about the club's position. We are prepared to sell for £25m.
"This offer stands for the next 10 days. If Mkhitaryan wishes to leave, they have to pay this amount for him."