The Toffees made a statement of intent by signing the England U21 international for £30m.
The deal will be finalised when Pickford returns from the European U21 Championships, which begins in Poland this week.
But according to The Mirror, Everton is looking to change the perception that they are not one of the Premier League's 'big clubs' by signing several more players.
Ajax captain Davy Klaassen is expected to complete his £25m switch to Goodison Park by the end of the week.
The Malaga forward currently has a £6m release clause in his contract and Toffees director of football Steve Walsh is working hard to negotiate a deal.