Mike Tye, currently deputy chief executive, is tipped to take over when Dyson – who has been at the firm for just one year – departs.
It is understood that Dyson feels his work at the pubs company is done, now that Spirit has demerged from debt-laden Punch Taverns. He is expected to depart before the end of the year.
Spirit declined to comment yesterday.
Spirit, which includes the Fayre & Square and Chef & Brewer chains, consists of the better performing managed pub business, with around 800 sites. The leasehold pubs continues to trade under the Punch Taverns name.
Earlier this month the new company reported strong fourth quarter sales growth although trading at Punch, which is grappling with net debt of around £2.5bn, has been tougher.
Dyson is a veteran of the leisure industry and has held executive roles at Rank Group, Hilton Group and Le Meridien, a division of Forte.
He was a highly-regarded finance director of Marks & Spencer from 2005 until last year, when he stunned the City by resigning in Marc Bolland’s first week as chief executive, having been passed over for the top job.