The Daily Express says Arsenal were interested in Danilo last week.
The London giants tabled an offer of £20m for Danilo on Wednesday, but Palmeiras turned the proposal down.
Instead, Arsenal will seek to revisit the situation in January.
The 21-year-old has a contract with Palmeiras to the 2026 season. He has scored twelve goals and produced nine assists in 128 competitive matches for the Brazilian club.