World Athletics usually stages the championships in August or September, which would typically clash with English football’s fixture schedule.
Replying to a post on X speculating that West Ham’s alleged stance could scupper London’s bid, Olympic 800m champion Hodgkinson saw the funny side.
“The GB team will bring back more medals to that stadium than West Ham have seen in their entire history,” Hodgkinson said.
She later returned to X to say she had “enjoyed the rattled comments” replying to her post and urged the club to “let us have this moment”.
“In all seriousness, to have a global championships back in London would be incredible for our sport. I didn’t think we’d get the opportunity again during my career,” she said.
Hodgkinson, who supports Manchester United, claimed her first World Indoor Championships 800m title in commanding fashion in Poland last week.
West Ham have won nine major trophies in their history, including three FA Cup titles and the 2022-23 Uefa Conference League.
They have had an underwhelming campaign this season with the club in the Premier League relegation zone, one point from safety.
The 62,500-capacity London Stadium was built for the 2012 London Olympics and is owned by London Legacy Development Corporation (LLDC).
West Ham left their former ground Upton Park in 2016 to move to the London Stadium and pay LLDC £2.5m annually as part of a 99-year lease for the ground.
The stadium has continued to host athletics events since West Ham’s move, including the 2017 World Athletics Championships and Diamond League meets.