Paddy asked former Arsenal boss, Unai Emery, to succeed Marco Silva, according to Sky Sports.
An unofficial meeting was held in London, and Emery is believed to want more time to think about his next steps, after his sack in the Emirate.
The Spaniard wants to continue improving his English as he sees England, as well as Spain and Italy, as viable options for his next job.
Everton are also believed to be keen on Shanghai SIPG boss, Vitor Pereira.
Chairman Bill Kenwright and majority shareholder Farhad Moshiri have drawn up a four-man shortlist, which includes Napoli manager Carlo Ancelotti.