The Villans made an offer of a straight loan which was rejected by The Hammers, per The Athletic.
It comes following reports that Villa boss Unai Emery is be keen to bolster his full-back department and provide competition for Matty Cash, and Wan-Bissaka is viewed as the ideal candidate.
Villa have failed to sign former Tottenham Hotspur full-back Emerson Royal, and have just let Kosta Nedeljkovic go to Rangers on loan with an option to buy.
Wan-Bissaka made 25 appearances for West Ham last season as they were relegated from the Premier League.
Recognised at one time as one of the best 1v1 defenders in world football, the DR Congo international has made 65 appearances in two seasons for the East London side.
He also made 190 appearances for Manchester United, winning the League Cup and FA Cup during his time at Old Trafford.
Now, Wan-Bissaka will be hoping to make a swift return to the Premier League, as Villa look to strike a deal with West Ham for his signature.