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.

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Newspaper reports have suggested the 33-year-old, whose deal at the Britannia Stadium expires at the end of the season, could join former Stoke boss Tony Pulis at The Hawthorns.
But Hughes said: "There's nothing in it. People are adding two and two together and making five.
"He's a big part of what we're doing here. His future is with us."
Crouch was signed by Pulis in September 2011, joining Stoke from Tottenham for £11m.
The striker - capped 42 times by England - has scored 29 goals in 117 Premier League games for the Potters and has attracted interest from elsewhere, most notably when linked with QPR in 2013.
Crouch has started all but one of Stoke's last six games and provided the header from which Ryan Shawcross scored the opening goal in the 1-1 draw against Manchester United on Thursday.
"You saw by his performance he wasn't bothered by any speculation," added Hughes.
Rather than offloading a forward in January, Stoke could be stretched by Mame Biram Diouf leaving to play for Senegal in the Africa Cup of Nations and Bojan's hamstring injury.
The former Barcelona man missed the draw with United, but Hughes is hopeful of a swift return.
"We have had Bojan checked," said Hughes. "He has a slight tear, grade one. It can be 10 days out or a couple of weeks. Hopefully he'll be back soon.
"We asked the Senegal FA about Diouf. They are within their rights to call him up on what I think is 5 January.
"We hoped to have him for the game at Arsenal, but they said no."

The Spain international has scored five goals in his last six games to help the Swans pull five points clear of the relegation zone.
Four of those have been headers, and Clement believes his aerial prowess compares to the world's best players.
"Llorente is wonderful at heading the ball," he said.
Clement continued: "[Cristiano] Ronaldo is also fantastic, [Gareth] Bale also good from a striker perspective.
"You have to look at John Terry and Sergio Ramos, central defenders who always did so well when they went forward into the box.
"He [Llorente] is doing very well and he's proven to be a key player during this period."
Clement worked with Ronaldo, Bale and Ramos at Real Madrid, while he coached Terry during his time with Chelsea.
Since taking over at Swansea, the former Bayern Munich and Paris St-Germain assistant manager has overseen five wins from eight Premier League matches.
That run of results has lifted the Swans from the foot of the table to 16th place, and Llorente has been pivotal to their upturn in fortunes.
A summer signing from Sevilla, the 32-year-old scored two goals to give Swansea a vital 3-2 win over Burnley on 4 March and take his personal tally for the season to 11.
"He's scored five goals since I've been here - the two at Liverpool, one at Chelsea and then the two against Burnley," said Clement.
"What's helped him is he's getting good supply into the box, and that was very clear in the game against Burnley - not just the two that he scored but other opportunities he had as well.
"He's a very good player when you get crosses into the box for him."
Meanwhile, Swansea will be without right-back Kyle Naughton for Saturday's trip to Hull with what Clement described as a "minor" hamstring injury.
The 28-year-old is expected to return for the match at Bournemouth the following weekend.
Aston Villa cannot stop midfielder Idrissa Gueye leaving the club after Everton triggered a release clause in the player's contract.
[NEXT_CONCEPT]
Stoke City manager Mark Hughes has dismissed speculation linking striker Peter Crouch with a move to West Brom.
[NEXT_CONCEPT]
Swansea City striker Fernando Llorente's form is "key" to their hopes of Premier League survival, says head coach Paul Clement.