The mid-market restaurant group shut three sites last year in Islington, Brixton and Newcastle, according to BigHospitality's sister site MCA.
The latest closure leaves it with six sites.
Backed by the Duke of Devonshire, property tycoon Nick Leslau and celebrity chef Loyd Grossman, Cabana Brazilian Bar and Grill is understood to have hired advisers from KPMG to review its options.
Barber has rebalanced the previously meat-heavy offer at the group.
He also runs Haché, the premium French burger restaurant group, with Ian Neill and Edward Standring.
Haché trades from six London sites and opened a seventh, in the former Cau site in Kingston-upon-Thames, in March with a wider menu.