Everton‘s valuation of £50m and the player’s hefty wage demands are seen as major stumbling blocks.
Barkley is keen on the prospect of joining Tottenham and linking up with his close friend Dele Alli.
He also sees a move there helping him regain his England squad place.
But West Ham are thinking big and want to make a statement with flagship signings.
They have already begun their summer recruitment by signing right-back Pablo Zabaleta, 32, on a free transfer from Manchester City – as predicted in the Daily Star Sunday two weeks ago.
Everton, meanwhile, are also keen on Ajax midfield ace Davy Klaassen, 24.
Klassen played in the 2-0 Europa League final defeat by United.