The 50-acre (20-hectare) spaceport is currently under construction at Boca Chica Village near the city of Brownsville, and is among four of the company's spaceports – others are located in Florida and California.
Proposed wall "cuts right through" SpaceX Texas
The remote Texas location is intended to be used for commercial launches from the US, including the Falcon 9 and Falcon Heavy rockets.
But the proposed route of the border wall would severely hamper these efforts, and has triggered concern from democrats, according to Bloomberg.
"This issue with SpaceX is that the fence cuts right through their property and that's a problem," said California congresswoman Lucille Roybal-Allard.
Representatives are now lobbying for the SpaceX site to be spared from the wall route, ahead of the scheme's final approval on 19 February 2019.
SpaceX refuses to comment
SpaceX and Musk, meanwhile, are reportedly refusing to comment on the situation about the Texas site.
Bloomberg added that company spokesman James Gleeson confirmed that the DHS and US Customs and Border Protection had visited the Texas hub, but refused to confirm whether the fence would affect the project.
"They are way behind the scenes on this, they are lying pretty low," said democrat representative Filemon Vela. "SpaceX doesn't want to offend DHS."
Dezeen also contacted SpaceX for a comment, but is yet to receive a response.
The conflict with SpaceX forms the latest in a string of controversies surrounding the Mexican border wall, which formed a key part of Trump's 2016 presidential campaign.
Follows controversies surrounding Trump's border wall
In December 2018, the US senate refused to fund the $5.7 billion (£4.4 billion) cost of the structure, which triggered the country's longest government shutdown in history.
The design of the barrier has also come under fire – a recent graphic of the proposed wall that Trump revealed on Twitter prompted ridicule from designers. It was also recently revealed that all of the eight prototypes of the wall failed basic tests.
SpaceX was established by Tesla founder Musk in 2002 with the aim to enable Mars colonisation and reduce space travel costs.
It also experienced its fair share of controversy last year, when Musk decided to use the company's technology to aid the rescue of a young football team stuck in a cave in Thailand. A backlash ensued when the head of the missioned claimed the rescue pod was "not practical", following which Musk took to Twitter to refute the claims.