The former Stamford Bridge boss has already included the 19-year-old in his Russian starting line-up five times.
And he told Blues owner Roman Abramovich to arrange a deal for the midfielder before his value increases.
Dzagoev is thought to be worth around £6 million but that price could double if his country qualify for next summer's World Cup and the player impresses at the tournament.
Russia coach Hiddink said: "He is young but with some improvement he will be ready for the Premier League within 12 months. I am convinced of that."
Dzagoev signed for CSKA two years ago and is already being compared to Andrey Arshavin, his compatriot at Arsenal.
The teenager played against Manchester United in the Champions League on Wednesday and will feature for his country in the play-offs against Slovenia.
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