The Hammers' season appeared to turn a corner last week when they won at Newcastle, but they have since suffered heavy losses to Arsenal and Leicester.
West Ham have four wins from 14 Premier League matches and are 14th in the standings, six points above the relegation zone.
Lopetegui has not been able to make them a competitive side and the pressure on him ramped up following their poor defeat at the King Power Stadium on Tuesday.
And if West Ham decide to make a change, Conceicao could be in contention for the job at the London Stadium.
Conceicao left Porto in June following a seven-year spell in which he won the Portuguese league title on three occasions.
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The 50-year-old, previously of Olhanense, Academica, Braga, Vitoria Guimaraes and Nantes, also has Champions League experience.
West Ham technical director Tim Steidten is understood to be a huge fan of Conceicao.
talkSPORT reported last month that he has become of interest to West Ham and other sides in the Premier League who may wish to change manager.
Conceicao is the latest name linked as a potential replacement for Lopetegui, who replaced David Moyes in the summer.
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Former Borussia Dortmund boss Edin Terzic has been sounded out by West Ham and is admired by club chief Steidten.
Terzic has past experience with the Hammers as he was an assistant coach to Slaven Bilic during his tenure from 2015 to 2017.
West Ham's defeat to Leicester was their seventh match in all competitions this season that they have conceded at least three goals.
Opposition sides have scored against them 27 times in the Premier League alone and they have a goal difference of minus nine.
Although their current league standing makes for disappointing reading, upcoming fixtures offer great chances to climb the table.
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Should Lopetegui remain in his job, his side will next host Wolves at home on Monday night.
West Ham then travel to Bournemouth before games against Brighton and Southampton either side of Christmas Day.
Following the defeat by Leicester, Lopetegui said: "It's not easy, because we deserved much more. We had 31 shots, many, many chances and we didn't score.
"We have to do better and avoid this stat. We had to take more risks in the second half and a good team will take advantage of this. We have to be more effective as normally when you are able to create this number of chances you are going to score one.
"We are very frustrated for the fans and players because they didn't deserve to lose.
"But we [lost] and we have to recover. The energy and belief for the next challenge is knowing this is the way to be able to change the situation."