The Hammers are preparing for the eventuality that the former Wolverhampton Wanderers manager cannot turn their poor start to the season around.
As previously reported, Hammers owner David Sullivan is keen to give Lopetegui more time.
However, the West Ham chief is alarmed at their record of only three wins from their first 11 Premier League games.
Director of football Tim Steidten is a big admirer of Terzic, who led Dortmund to last season's Champions League final.
The 42-year-old worked as a scout and coach for Dortmund's academy during ex-Liverpool manager Jurgen Klopp's time at the club.
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He then served as Slaven Bilic's assistant at Turkish club Besiktas between 2013 and 2015, before the pair went to West Ham together.
They were at the club between 2015 and 2017.
West Ham finished seventh and 11th, with his second season being the club's first at the London Stadium.
Bilic was sacked after a poor run of results at the start of the 2017/18 season.
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Terzic left with him, then returning to Dortmund as a coach in 2018.
He served as interim manager at the end of the 2020/21 season, and became permanent boss ahead of the 2022/23 campaign.
Last season, he guided the club to fifth place, as well as the Champions League final.
However, they were beaten 2-0 by Real Madrid in the showpiece event at Wembley in June.
Despite being contracted until 2025, Terzic left the club at the end of last season, citing a desire to allow the club to begin a new era.
Lopetegui has already under pressure this season, with the Hammers sitting in 14th in the table.
They are five points above third-from-bottom Crystal Palace.
Last season they finished ninth, waving goodbye to long-serving manager David Moyes.
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While the West Ham hierarchy have already began to sound out alternatives for Moyes' successor, talkSPORT's Rory Jennings has tipped Ruud van Nistelrooy to take over.
The former Manchester United star, who just finished his interim manager spell at Old Trafford, is now available.
West Ham then host Arsenal at the end of the month.