BBC Sport says the former Wolves manager has verbally settled on a deal with West Ham. However, nothing has been signed.
Current Hammers boss David Moyes is off contract at the end of the season and has always maintained his situation won't be settled until the summer.
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Former Spain and Real Madrid coach Lopetegui was in talks with AC Milan before supporter protests ended contact last week.
The Spaniard quit Wolves in August after being left disappointed with transfer spending.