Allardyce has been Blackburn boss since December 2008
The Indian businessman interested in taking over Blackburn has had his "period of exclusivity" extended.
Ahsan Ali Syed's Bahrain-based firm Western Gulf Advisory (WGA) was granted exclusive negotiating rights by the Ewood Park club last month.
It means no other potential buyer can take over the club while WGA continues to explore options.
"WGA remains committed to pursuing the opportunity to acquire such a prestigious club," said a statement.
"But the due diligence process is taking longer than originally envisaged."
Syed reportedly has £300m to take over Blackburn, cover outstanding debts and "provide the necessary capital to buy new players and invest over the longer term so it can once again become a title contender", according to a statement he released last month.
However, BBC Radio 5 live reported in August that the business has been ordered to cease trading by Bahrain's trade and commerce ministry for allegedly violating regulations by operating outside its remit.
WGA insisted the Blackburn bid was being managed by a separate company and was unaffected, but Blackburn manager Sam Allardyce said last week that the prospect of a takeover seems doubtful.
Syed, a 36-year-old lawyer, told BBC Radio Lancashire when takeover talks were announced: "I am very keen to move very fast and buy this club at the earliest moment.
"I am aware that 'Big Sam' has big ambitions for this transfer window and I would love to support his ambitions."
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