The club have also parted company with Lopetegui's backroom staff, including his assistant Pablo Sanz, head of performance Oscar Caro, head analyst Juan Vicente Peinado, fitness coach Borja De Alba and technical coach Edu Rubio.
"The board would like to thank Julen and his staff for their hard work during their time with the Hammers and wish them every success for the future," the club's statement added.
"The process of appointing a replacement is under way."
Former AC Milan boss Paulo Fonseca and ex-Paris St-Germain manager Christophe Galtier, currently in charge of Saudi Pro-League club Al Duhail, have also been spoken to by West Ham.
However the belief from both camps is that Potter will get the job.
West Ham's next game is an FA Cup third-round tie at Aston Villa on Friday.