The Yorkshire club are looking to bolster their central defence this summer having sold Pontus Jansson already.
Marcelo Bielsa is looking to find a suitable replacement and has targeted the Welsh defender. The report claims that Leeds are even ready to pay £7.5m for the 35 times capped defender.
The 30-year-old is currently out in the United States with the rest of the Villa squad.
Chester has a wealth of Championship and Premier League experience and would be a superb addition to the Leeds squad. However, whether the player would agree to drop down the league remains to be seen.
Villa have bolstered their defence this summer with Dean Smith bringing in as many as four new players to compete with Chester in the coming Premier League campaign.
In fact, Smith has stated that Chester is a key player for his side, and he is very much a part of his plans.