Bosses at the supermarket giant agreed the takeover move, led by institutional investor Fortress, earlier this month.
However, on Tuesday evening, Morrison’s largest shareholder, Silchester International, said it will not support the offer and called for more time for other potential bidders to come forward.
The current agreed deal values Morrisons at 252p per share, with a conditional special dividend of 2p per share.
On Wednesday, the Singaporean GIC fund said it will take part in the consortium to buy Morrisons via its Cambourne Life investment vehicle.
Fortress will continue to hold a majority position in the consortium and the value of the takeover offer will remain unchanged.
It comes around a week after private equity firm Apollo said it was in talks to join the Fortress-led agreed takeover deal.
Morrisons shareholders are currently due to vote 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 £5.5 billion 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.
Morrisons’ share price was more than 265p on Wednesday morning, firmly ahead of the 254p takeover offer, suggesting that investors believe a higher bid is still likely.