Calvert-Lewin has been unavailable for much of the season due to injury, but has been in impressive form for Everton since breaking out of the club academy and scored three goals in three games before fracturing his toe in late August.
The striker also scored 16 times in the Premier League last season, earning him a spot in the England squad for Euro 2020.
Calvert-Lewin suits the player-profile Arsenal are looking for as they try to rebuild their squad, with the striker only 24 years old.
Everton, however, are likely to fight very hard to keep the player as they too are looking to rebuild and get back towards European qualification.
Lille forward David, who is currently the top scorer in Ligue 1, is another player that Arsenal have watched this season.
The Gunners have been tracking the Canada international for a long time and they scouted him when he was playing for Gent, who he left to join Lille in 2020.
Like Calvert-Lewin, David fits the profile Arsenal are after as he will not turn 22 until early next year.