The 25-year-old first emerged as a target for Boro in the summer of 2013, but they failed to land him as they made a move towards the end of the transfer window.
Now the Championship club have returned with a new offer of €4million (£3.1million), but Genk have been quick to say no, insisting they turned down nearly twice that amount in January.
"A bid of €4million is not enough for a player of this calibre, remember that certain players have even joined us before for €10million (£7.9m)," Genk chairman Herbert Houben told Het Nieuwsblad.
Genk promised Vossen that they would listen to offers for him this summer, but Houben insists that does not mean they will be letting him leave on the cheap having already rejected a €7million (£5.6m) bid from Rubin Kazan earlier this year.
"We want to fulfil our promise, but that does not mean we have to let him go for anything," he continued.
"There was a more lucrative offer from Russia [in January] at which point we agreed with Jelle to cooperate, but only at that level or similar, but there has been no bid like that yet.
"I firmly believe in the next few weeks and months, better offers will come.
"I understand that the less a club gets the more the player gets and perhaps he is being hunted and promised heaven, but things have a come a long way if it is a player that determines where he will play."
The player's father Rudi Vossen looks after his son's interests and he admits that he hopes a resolution will be found.
"We wait, we hope for common sense from Genk and that it will not just brush off clubs and Jelle will be able to leave in a nice way."
Vossen scored 12 goals for Genk last season and has also been linked with West Ham United in recent weeks.