The consortium, led by Majestic Wine owner Fortress, has said the Competition and Markets Authority (CMA) told the bidder it "has no further questions" regarding the offer.
In a statement to the stock market, it added that the CMA has "not opened an inquiry or indicated in writing that it is still investigating whether to open an inquiry".
It comes after the collapse of Sainsbury's agreed mega-merger with Leeds-based Asda in 2019 after the CMA blocked the deal.
Earlier this year, Asda agreed to sell 27 petrol forecourts in order to help its £6.8bn acquisition by the Issa Brothers and private equity backers TDR Capital secured approval from the watchdog.
The Morrisons bidder said that it does not expect any delay in proceeding with the agreed takeover, which will go to a shareholder vote next month.
Investors will have their say on the offer, which was supported by the firm's board of directors, at a general meeting on August 16.
The retailer agreed to the takeover move days after it rebuffed an initial £5.5bn approach from rival private equity firm Clayton, Dubilier & Rice (CD&R).
UK takeover regulators have given CD&R a deadline of August 9 to either place its own firm bid for the chain or walk away.
However, a number of major Morrisons shareholders, including its largest investor Silchester International, have criticised the agreed deal.
On Tuesday, Silchester said it will not support the offer and called for more time for other potential bidders to come forward.
Fellow shareholders M&G and JO Hambro have also suggested the current move is valued too low.
Shares in the company are currently valued at over 264p per share, suggesting that shareholders believe there is still strong potential for a rival bid above the 254p per share offer made by the consortium.
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