According to the Daily Mail, Silva is impressed by what he has seen from the Scotsman in recent months.
Other clubs with an interest include Norwich and Cardiff.
Silva knows Bowen from his time at Hull, where he gave the player his debut in the Premier League.
The versatile attacker has 19 goals in 37 games in the Championship this season.
The 22-year-old would add depth to the Toffees' attack as they make preparations for next season.