Benteke's representative, Eris Kismet, revealed the "dream" of the 21-year-old to play in the Barclays Premier League.
But Genk have turned down what Kismet describes as "a very good bid" for the Belgium international.
Kismet told Press Association Sport: "It is not true to say he (Benteke) has gone on strike - but he is not happy with the situation either.
"Very simply, he wants to go and play in England, in the Premier League. That is his dream.
"You play football to make an impression so you can live your dream and when the football club is not being co-operative, you have got a problem.
"Aston Villa have made a very good bid and it has been refused. Will they make a new bid? The big issue is how Genk behave. It is the dream of every player to play in the Premier League."
Benteke has been watched on several occasions by Villa and manager Paul Lambert has stepped up his interest and hopes to conclude a deal before the transfer window shuts on Friday.
The player has netted three times in five games this season after being on target 18 times during the 2011-12 campaign in all competitions. He also scored for his country for the first time in the 4-2 win over Holland earlier this month in what was his fifth appearance.
Villa are also believed to be interested in another striker in Ivory Coast international Yannick Sagbo, who is currently on loan to French top flight side Evian from Ligue 2 Monaco.
- Barclays Premier League
- Aston Villa