The 58-year-old was appointed as Hammers boss in July following the departure of David Moyes at the end of last season, but he has struggled to make the desired impact at the club.
West Ham spent over £120m on nine new players in the belief that Lopetegui could steer the club towards a return to Europe, but they are currently languishing in 14th place in the Premier League table and are closer to the relegation zone than the top seven.
Lopetegui's position at West Ham has come under intense scrutiny following Tuesday's 3-1 defeat away against Leicester City - the Spaniard's eighth defeat in 16 games across all competitions since his arrival.
Despite calls from some of the club's supporters for him to be sacked, Lopetegui will remain in charge of West Ham for a must-win Premier League contest at home against his former club Wolverhampton Wanderers next Monday.
However, multiple reports have suggested that defeat would spell the end of his brief reign in East London, and former Chelsea head coach Graham Potter is reportedly one name high on their shortlist of potential targets.
Lopetegui: 'We are going to change the situation'
Lopetegui arrived at West Ham's training ground early on Thursday morning as planned and led the first-team training session while the club's hierarchy held a meeting to discuss his position at the club.
Speaking at a pre-match press conference on Friday, Lopetegui insisted that he, his players and his staff "are going to change the situation" and will be ready for the "important challenge" against Wolves.
"I have a big commitment in my work as always," Lopetegui told reporters. "I am very happy to stay at West Ham. We are going to change the situation. That is why we are working, to be ready for Monday."
Asked whether he believes he has only one game to save his job, Lopetegui added: "I am not thinking this. We have one very important challenge on Monday against a good team.
"They have very good players and good coach, so we have to focused to develop our work until Monday to be ready, to give our fans a good day."
Lopetegui plays down Todibo bust-up rumours
Meanwhile, reports earlier this week have suggested that Lopetegui and West Ham defender Jean-Clair Todibo were involved in a bust-up at half time of last weekend's 5-2 home defeat to Arsenal.
Todibo was subsequently left out of the matchday squad for Wednesday's loss to Leicester, but Lopetegui has revealed that the Frenchman's absence was due to injury.
Asked if he has fallen out with Todibo, Lopetegui said: "The things that happen in the dressing room have to stay in the dressing room. Always.
"I don't know exactly what you want or what you though, but nothing important happened."
The Hammers boss added: "The players have been fantastic. [Great] commitment. I don't have anything to say against my players.
"I will not talk bad about my players, I accept all the responsibility and pressure. That is why I am the coach. My players have to enjoy their profession. They are demanding with themselves and to believe in them is the most important thing."
Todibo is a doubt for West Ham's encounter with Wolves, as is striker Danny Ings who picked up a knock in midweek and will be assessed ahead of kickoff.
Written by
Oliver Thomas