Laragrove, one of the two firms interested in taking over Debenhams, has dropped out of the fight for the department store group.
The decision leaves the way clear for the consortium Baroness Retail, led by private equity group CVC Capital Partners, to buy the group.
Laragrove said it would not be raising its £1.5bn offer for the group after the consortium Baroness Retail upped its bid to £1.72bn.
Laragrove, led by investment group Permira, said the offer proposed by Baroness exceeded the price it was prepared to pay.
Earlier, CVC and Texas Pacific said their Baroness Retail operation had raised its offer for the high street chain by 3.3%, or 470p per share.
Baroness was effectively bidding against itself with the latest offer as it topped a £1.66bn, or 455p a share bid, which it tabled last month.
Knock-out blow
Last month, Debenhams recommended a £1.66bn offer for the firm from Baroness after withdrawing its support for an earlier bid from Laragrove.
Industry observers said Baroness Retail had tabled the new offer in the hope that it would prove to be the knock-out blow in the battle for Debenhams.
Its rival Permira, lost the backing of US investment bank Goldman Sachs this week, and has been busy trying to plug the funding hole.
Permira kicked off the bidding war for the store group in May with a £1.54bn offer.
Laragrove's decision to pull out of the running for Debenhams comes only days before an 31 October deadline set by the Takeover Panel.