Mikel Arteta's side enquired about the 21-year-old in the summer but were told Palmeiras had no interest in selling while pursuing their 11th Brazilian Serie A title, which they then claimed at the beginning of the month with a 4-0 win over Fortaleza.
Sources have told ESPN that Palmeiras have since softened their stance, which has led Arsenal to revive their interest as they search for a central midfielder to strengthen their squad.
Palmeiras own 80% of the player's rights and sources suggest they are seeking €20m for Danilo. His boyhood club Cajazeiras own the other 20% but there is said to be confidence fee for their part could be negotiated, making the overall fee lower than €24m, depending on talks.
Arsenal are in contact with Palmeiras but face competition from Ajax, who are believed to be ready to table a formal offer ahead of the January window.
Monaco are among several other clubs to have contacted Palmeiras and have so far expressed the most interest of the chasing pack.
Sources have told ESPN that Arsenal are keen on adding a central midfielder and a winger if possible in January with the club's owners ready to back Arteta as they attempt to launch a bid for the Premier League title.
Arsenal won their final game before the World Cup break at Wolverhampton Wanderers to move five points clear at the top of the table.