News of the World reports that Begiristain will join the club if a power-sharing agreement with manager Carlo Ancelotti can be reached.
Chelsea owner Roman Abramovich is keen to bring in Begiristain in order to be able to sign Fernando Torres and win the Champions League.
Begiristain won the Champions League twice as a sporting director at Barcelona.
Chelsea want Begiristain to make a move for £40million-rated Liverpool striker Torres.
