But talkSPORT claim a rival bid from Liverpool is being prepared, while Juventus are also keen.
Chelsea target Miralem Pjanic in action
Juve are willing to offer £26.6m plus striker Simone Zaza to land the former Metz and Lyon ace.
Liverpool are themselves pushing to sign a number of players during the summer transfer window, with Poland's Piotr Zielinski on manager Jurgen Klopp's radar.
As for Chelsea, they are also interested in signing Pjanic's midfield team-mate Radja Nainggolan and defender Kostas Manolas.
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