The Bradford-based grocer said it received the "unsolicited, highly conditional non-binding" proposal of 230p a share on Monday.
Britain’s fourth largest grocer after Tesco, Sainsbury’s and Leeds-based Asda, said it rejected the proposal on Thursday.
The group said in a statement: “The board of Morrisons evaluated the conditional proposal together with its financial adviser, Rothschild & Co, and unanimously concluded that the conditional proposal significantly undervalued Morrisons and its future prospects.
”Accordingly, the board rejected the conditional proposal on 17 June 2021."
Shares in Morrisons, which are down 5.5 per cent over the last year, closed on Friday at 182p, valuing the group at £4.33bn.
Morrisons said CD&R’s proposal provided for Morrisons shareholders to still receive the final dividend of 5.11p per share which was announced on March 11.
CD&R had earlier said it was considering a possible cash offer for Morrisons.
Under takeover rules, CD&R has until July 17 to announce a firm intention to make an offer.
CD&R’s approach underlines private equity’s growing appetite for UK supermarket assets, attracted by their cash generation and freehold assets.
In February, brothers Zuber and Mohsin Issa and private equity firm TDR Capital purchased a majority stake in Asda from Walmart in a deal valuing the UK supermarket group at £6.8bn.
That deal followed Sainsbury’s failure to take over Asda after an agreed deal was blocked by Britain’s competition regulator in 2019.
Morrisons has a partnership agreement with Amazon and there has been speculation it could emerge as a possible bidder.
A formal bid from CD&R could involve Terry Leahy, the former Tesco CEO, who is a senior adviser to CD&R.
When at Tesco, Mr Leahy oversaw Andrew Higginson and David Potts, who are now Morrisons’ chairman and CEO respectively.
Morrisons has about 500 stores and 118,000 staff, making it one of the country’s biggest private sector employers.
In March, the group reported a halving of annual profit due largely to costs incurred during the Covid-19 pandemic, but forecast a bounce back in its 2021-22 year.