The Ukrainian defender could feature for Barca against Real Zaragoza at Camp Nou on Sunday.
Chygrynskiy has been out of action since September due to a knee ligaments injury.
Sport says Barca coach Pep Guardiola is keen to pair Chygrynskiy with Gerard Pique at the back.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.