Marquinhos joined the Gunners from Sao Paulo in a £3million deal in the summer and has made four appearances this season, scoring one goal against FC Zurich in the Europa League.
But the 19-year-old has made just one substitute appearance in the Premier League and Arsenal are now considering his situation ahead of the January transfer window.
The Gunners looked at loaning Marquinhos out when he joined in the summer but decided he would stay and get some action in the Europa League.
Arsenal will now decide whether to keep him in their squad for the second half of the season or send him to another club to get first-team experience.
Marquinhos could end up staying put, with Arsenal facing a hectic schedule after the World Cup. The Carabao Cup fourth round is due to start just two days after the World Cup Final, while the quarter-finals and both legs of the semi-finals are in January. The third and fourth rounds of the FA Cup are also in January.
Marquinhos could easily be involved in those games and, as a result, Arsenal are unlikely to sanction a loan if it will leave them short on numbers.
Arsenal are not flush with wide options and are interested in signing a new winger in January if they can find a player who will improve the squad for the right price, with interest in the likes of Facundo Torres at Orlando City and Shakhtar Donetsk star Mykhaylo Mudryk.