Ahsan Ali Syed's firm Western Gulf Advisory's (WGA) agreement with Rovers means no other potential buyer can take over the club while the company continues to explore options.
A statement from WGA said: "Western Gulf Advisory announces that the period of exclusivity it was granted in order to conduct due diligence on Blackburn Rovers Football Club has been extended.
"This enables WGA to continue to explore the financial situation of the club while ensuring that no other bidder can buy it or look into its books.
"Although the due diligence process is taking longer than originally envisaged WGA remains committed to pursuing the opportunity to acquire such a prestigious club."
WGA is based in Bahrain and Switzerland, though chances of a takeover appeared to have receded after allegations about Syed's finances were made in a BBC documentary.