The centre-back is believed to have a £29.5m release-clause and could be the subject of a bid as early as January.
However, should Moyes wish to splash the cash on the German international he would face stiff competition from Barcelona who see the ball-playing centre-half as the natural successor to the ageing Carles Puyol.
The 24-year-old has established himself alongside defensive partner Nevan Subotic as one of the best defenders in Bundesliga.
Hummels also has 26 caps for Germany and could spark a bidding war between Europe's top clubs.
Catalan club Barcelona may be the initial favourites for the player's signature, with the former Bayern Munich youngster previously stating his interest in a move there.
"Barca is one of the clubs that would interest me," Hummels is quoted as saying in the Express.
Should Dortmund lose their star man, they may rival Arsenal for reported target Fabian Schar.
The FC Basel defender has also attracted interest from Serie A outfit Juventus.
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