The Senegal international, 26, joined for £9m from Lille in July 2015 and played 35 times as Villa were relegated from the Premier League last season.
Other interested clubs have until the end of July to make a bid for Gueye.
"If he wants to go, we are powerless," club chairman Dr Tony Xia posted on Twitter.
Gueye only missed three league games for Villa in 2015-16 and scored his only goal for the club in their FA Cup fourth round win against Wycombe in January.
It is believed the fee that has activated the departure clause is about £7m, with Villa bracing themselves for further offers.
Aston Villa cannot stop midfielder Idrissa Gueye leaving the club after Everton triggered a release clause in the player's contract.