Morrisons has announced it is in talks with both of its US private equity suitors, as well as the UK’s Takeover Panel, which regulates acquisition activity, to begin an auction procedure to settle who takes control of the country’s fourth largest supermarket chain.

Last month, the board of the grocer recommended that shareholders back an offer by Clayton, Dubilier & Rice (CD&R) that would value the supermarket chain at £7bn (or £9.7bn including debt).

However, it is thought that the rival private equity firm Fortress, owned by the Japanese investment bank SoftBank and which has had its offers of £6.5bn and £6.7bn trumped by CD&R, could still come out with an improved bid.

Morrisons said in a statement that it was working on the basis that neither firm had declared its offer to be final, and “such that either offer may be further increased or otherwise revised, a competitive situation continues to exist”.

It added that it was beginning “discussions around an orderly framework for the resolution of this competitive situation” through an auction, which will take place before 18 October on a date yet to be announced by the Takeover Panel. The supermarket chain will then decide whether to recommend the CD&R or Fortress offer to its shareholders.

Morrisons intends to send a document to shareholders on or around 25 September, containing more information about CD&R’s offer, which values the firm at 285p a share, as well as notice of a meeting to approve the offer. If the board backs an improved Fortress bid instead, it will hold a meeting to improve this offer.

Sign up to the daily Business Today email or follow Guardian Business on Twitter at @BusinessDesk

A shareholder meeting to approve either the CD&R or Fortress offers – depending on which one Morrisons backs – is scheduled for a date in the week beginning 18 October.

The supermarket chain said it would not only consider the financial terms of any offer, adding: “The Morrisons board continues to place very significant emphasis on the wider responsibilities of ownership of Morrisons”, which include “recognition of the importance to the Morrisons business of all stakeholders, including colleagues, customers, pension trustees and suppliers as well as the distinct heritage and history of Morrisons and the legacy of Sir Ken Morrison”.

Trustees of its pension schemes have previously warned that CD&R’s £7bn takeover of the chain threatens to “materially weaken” their financial position, leading them to demand additional security over some of the supermarket’s assets.