The English newspaper claims Arsenal are closing in on a deal with Adli which would see him move to London on a three-year contract.
The young Frenchman is available after he rejected professional terms with Paris Saint-Germain and it is thought Emery could be a big decider in any potential transfer.
Emery gave Adli his first-team debut toward the end of last season, bringing him on as an 83rd-minute substitute in PSG's league game against Caen.
The 17-year-old has been capped at three different age groups by France and is considered to be one of the best young players in Ligue 1.
Arsenal will need to convince Adli that his development will be best served at the Emirates and with the club actively looking for new players and already making waves in the transfer market, that could be easier to do.