According to the source, the Gunners have been monitoring the progress of the 21-year-old Ukrainian for a long time, but at this stage they have not yet made an official offer to Shakhtar.
The north London club are keen to sign Mudryk, but the Donetsk outfit are currently looking to cash in on €60-65m from the sale of their player, so a deal will be difficult.
Due to the great interest in the Ukrainian from other clubs, the Gunners need to act quickly if they want to complete this transfer.
The Italian journalist also reports that Arsenal have an alternative option in Orlando City winger Facundo Torres if they fail to win the battle for Mudryk.
According to the Transfermarkt portal, the 22-year-old Uruguayan is valued at 7 million euros (Mudrik has 15 million euros). Torres has 40 matches, 13 goals and 10 assists for the American club, while the Ukrainian has 40 matches for Shakhtar, 9 goals and 16 assists.