The television personality was hurt in December while at the Top Gear test track at Surrey’s Dunsfold Park Aerodrome, according to The Sun.
Along with another crew member, Flintoff was seriously injured when a Morgan Super 3 - an open-topped three-wheel sports car - flipped in December. The car has a top speed of 210km/h.
The former professional cricketer, 45, experienced severe facial wounds and broke several ribs.
Shortly after an investigation into the incident, the BBC publicly apologised to the star and announced that the show would not continue.
“Under the circumstances, we feel it would be inappropriate to resume making series 34,” a spokesperson said.
“We understand this will be disappointing for fans, but it is the right thing to do, and we’ll make a judgment about how best to continue later this year.
“This has also impacted the production team, who we continue to support. Finally, there will be a health and safety review of the show, in line with our procedures.”
The presenter received medical treatment on site before being rushed to hospital.
“We have sincerely apologised to Freddie and will continue to support him with his recovery,” the BBC announced.
The Morgan Super 3 that Flintoff was driving was allegedly not fitted with airbags, The Sun reported this month.
The television star has suspended all work until he makes a full recovery.
“The full extent of his injuries will surprise many people, as the details of what happened have yet to fully emerge,” an insider revealed to The Sun in January.
“He is putting his career on hold until he is in a better place, mentally and physically, and can’t say when he will return to making TV shows.
“As a loving husband and dad he understands the fear his family feel about what’s happened, knowing that he could have been killed.
“He is determined to resume his TV work at some point though.
“That’s why this decision will be a painful one for Freddie, but he knows that, for now at least, there are more important things in life.”