The Spaniard will be taking over from David Moyes now that the Premier League season has concluded.
Lopetegui, per The Express, has already agreed a deal in principle to take charge from the summer onward.
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The ex-Spain, Real Madrid, and Wolves boss wants to see the club spend significant sums on new players.
Moyes departs West Ham after four and a half very successful seasons in charge.
The Hammers won the Europa Conference League during his time at the helm.