A spokesperson for Barclays Center and FCRC declined comment on the report.
The terms of the deal are still unknown, but the NBA is in the process of reviewing the deal, per the report.
Prokhorov already owned 80 percent of the Nets and 45 percent of Barclays Center as part of his original deal in May 2010, and there have been constant rumors since that Prokhorov would eventually assume full ownership in the past year.
Prokhorov is also expected to attend Nets games next week, which may coincide with an announcement regarding his ownership.
More to come as this story develops.