According to reports from Mexico, the Premier League side have made contact with Tijuana's hierarchy as they explore the possibility of signing the attacking midfielder in the winter transfer window.
Mora has a reported release clause of $28 million in his contract, giving Arsenal a potential route to securing one of Mexico's most highly rated young players.
The 17-year-old has also been linked with Real Madrid, Barcelona, Liverpool, Borussia Dortmund and Benfica, setting up the possibility of competition for his signature if the reported interest develops into formal offers.
Tijuana secured Mora's future with a three-year contract in June, an agreement the club described as a landmark deal in its history. He was also handed the number 10 shirt, underlining the importance of the academy graduate to the Mexican side.
Arsenal have increasingly looked towards emerging talent as they plan for the future, and Mora would represent another investment in a young player with significant room to develop.
A January transfer would depend on whether the clubs and player can reach an agreement, with the reported release clause likely to be a central factor in any negotiations.
For now, the reported approach signals Arsenal's interest rather than confirmation that a deal is close. Tijuana's stance and Mora's own preference will help determine whether the London club can turn their initial contact into a transfer.
The competition for the teenager's signature could be considerable, with the reported list of interested clubs including some of Europe's biggest names. Arsenal will need to convince Mora that north London is the right place for the next stage of his development if they decide to pursue the move.
No agreement has been announced, and the reported January approach remains an early step in a potential transfer.