The Guardian reports that the two men first met last year, when Fayed demanded £2bn for the store.
Green was not interested at that price, but the paper said that now Fayed has moved to Geneva - for what it describes as tax purposes - the Egyptian could be ready to accept a more realistic figure.
Green denied the report in an email to the paper which said: “At no time in the past have there been any discussions between myself and Al Fayed concerning the sale of Harrods. I trust this ... will put an end to this speculation and lay this matter to rest.”
Dairy Crest is to cut 80 jobs when it closes its butter and milk powder operations at Chard in Somerset in July, at a cost of £14m.