ESPN Brazil reports that discussions have taken place over the defender, although Arsenal face competition from other interested clubs whose identities have not been disclosed.
Ryan has recently stepped up to Bragantino's senior side and has also represented Brazil at Under-20 level this year. His progress has brought him to the attention of European scouts as Arsenal assess whether he could eventually develop into a first-team option.
The Gunners have a history of monitoring emerging Brazilian players before their value rises, and ESPN has drawn comparisons with the recruitment process that led them to sign Gabriel Martinelli in 2019.
Arsenal tracked Martinelli while he was playing for Ituano in Brazil's third tier and moved to secure his signature before he turned 18. The club's interest in Ryan suggests they remain keen to identify promising players early in their careers.
Martinelli has since left Arsenal for Al Hilal, but his original move to north London remains an example of the club's willingness to recruit outside Europe's established leagues.
Ryan's situation is different because he has already made the step into senior football and is old enough to move to England. His experience with Bragantino and Brazil's youth side provides Arsenal with opportunities to assess his development beyond academy level.
ESPN Brazil also outlined the broader principles behind Arsenal's scouting in South America. The club reportedly values technical ability when assessing Brazilian prospects, while considering competitiveness and determination important characteristics in players from Argentina and Uruguay.
The report suggests Arsenal also examine the balance of technical and physical qualities among players in markets such as Ecuador and Colombia, with their potential to adapt to the Premier League an important consideration.
The club is said to track some youngsters from around the age of 14, particularly those who stand out in academies and youth international teams. Attention is currently focused on players born in 2008 and 2009, although international transfers to England are subject to age-related restrictions.
Ryan, at 19, would not face the same minimum-age barrier as younger prospects if a move were agreed.
The reported informal discussions do not mean a transfer is imminent, and no agreement has been announced. Arsenal's interest will need to develop into a concrete proposal if they are to bring the right-back to England.
For now, Ryan's emergence at Bragantino and his involvement with Brazil's Under-20 side have put him on Arsenal's radar as the club continues to look for potential recruits in South America.