Boro have a long-standing interest in the Belgium international striker having first made a move for him in the summer of 2013.
They returned with a €4million (£3.2m) bid over the weekend, but that was quickly rebuffed by Genk and the offer drew criticism from their chairman Herbert Houben.
Genk, who turned down €7million (£5.6m) from Russian club Rubin Kazan in January, want closer to €10million (£7.9m) for their captain, but the player is far from happy with the club's stance and wants them to let him leave.
"I'm bitterly disappointed at what Genk's president said. He gave the impression it's all about the money. I'd expected some more respect," Vossen told Het Belang van Limburg.
"In January, Rubin Kazan had offered Genk seven million plus add-ons. Genk rejected it and I didn't make a war. We've made the agreement that if there was a good bid in the summer, I would be allowed to go.
"We put an amount on paper and I must admit it's higher than four million [which Middlesbrough offered], but there was that promise. It's a shame they don't want to fulfil it.
"Four million is a good amount for a Belgian striker, and the add-ons aren't included. If they're waiting for a bid of seven million, they could be waiting for a long time. Certainly after last season. I've lost my place in the World Cup squad and we aren't even playing in the Europa League. I'm ready for a transfer abroad and I would find Middlesbrough a good challenge."