According to The Telegraph, Leahy, who is also a senior advisor to CD&R, is being considered for the role due to his previous experience with Tesco.
However, the paper also cautions that sources have said currently he is only being considered for the role and it could yet appoint another candidate.
If the reports are true, he would replace current chairman Andrew Higginson. The Telegraph also cites that if the CD&R deal is to go ahead, the private equity firm would also appoint its executives Marco Herbst and Gregory Lai to the board of the grocer.
The news comes after it was revealed Morrissons had accepted a new £7bn offer from CD&R.
In a statement on Thursday evening, the big four grocer revealed it had accepted the deal which values the business at 285p per share, an increase of 13p per Morrisons Share and £332m total offer value on the terms of the rival Fortress offer.
Morrisons directors said they intend to “recommend unanimously” that Morrisons shareholders vote in favour of the deal at a general meeting which is expected to take place in or around the week commencing 4 October 2021.
Andrew Higginson, chair of Morrisons, said: “The Morrisons board believes that the offer from CD&R represents good value for shareholders while at the same time protecting the fundamental character of Morrisons for all stakeholders.
“CD&R have a strong record of developing, strengthening and growing the businesses that they invest in and they share our vision for Morrisons’ future. This, together with the strong set of intentions that they have set out today, gives the Morrisons board confidence that CD&R will be a responsible, thoughtful and careful owner of an important British grocery business.”
Sir Terry Leahy, senior adviser to CD&R funds, added: “CD&R is delighted to have the opportunity to support the management of Morrisons in executing their strategy to grow and develop the business. The grocery sector in the UK is undergoing great change and we believe Morrisons is well placed, with CD&R’s support, to succeed in this environment.”
In response to the deal, rival firm Fortress released a short statement confirming it is “considering its options” and urges Morrisons shareholders “to take no action”, adding that a further announcement will be made in due course.