The 22-year-old has made 79 appearances for RBL since arriving from New York Red Bulls in 2019, including 13 outings in all competitions during the 2021-22 campaign.
Adams has a contract with his Bundesliga club until June 2025, but there is believed to be a €40m (£34m) release clause in his deal.
According to Bild, Arsenal are planning to move for the United States international either in January or during next summer's transfer window.
The report, though, claims that the Gunners would have to pay €40m (£34m) to sign him, as Leipzig would not be prepared to discuss any offer under his buy-out figure.
Adams has shown his versatility by operating as a holding midfielder, right-sided midfielder and right-back during the 2021-22 campaign, which has included four appearances in the Champions League. body check tags ::