The France international has been on Barca's transfer list since the end of last season, but has generated little interest.
Umtiti has managed just six appearances this term - all from the bench - but Zenit are prepared to move for him this summer.
Sky Italia says Zenit are in contact with Barca and Umtiti, but the player is hesitant over accepting a move to Russia.
Should he agree, Umtiti would be reunited with former teammate Malcom at Zenit.
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