Gunners head coach Mikel Arteta is said to be an admirer of Soler, who has become a key performer for Los Che over the past few seasons.
Arteta is keen on signing players from his native Spain this summer as he looks to improve his squad.
Soler is under contract at the Mestalla Stadium until 2023, although it's believed Valencia need to sell this summer to balance their books.
It's thought they must raise £36m and the sale of the 23-year-old would go some way to achieving that amount - if not fulfilling it.
There is no indication of how much they would want for Soler as things stand.
Barcelona held discussions over signing Rodrigo from the Mestalla in January, although nothing eventually came of it as they secured Martin Braithwaite instead.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.