Hungary international Varga enjoyed a season-long loan spell at The Riverside from Debrecen last season and ended the campaign as first-choice right-back under Aitor Karanka.
Boro were keen on keeping the 25-year-old, but Varga claims that finances have blocked a deal being done.
"I know what the truth is because I was speaking with my agent (Vladan Filipovic), he had negotiations with Middlesbrough and the reasons of my departure are not connected with my performance," said Varga, speaking at a press conference ahead of Hungary's friendly with Denmark on Thursday.
"It seems their budget doesn't allow them to buy me permanently, and this is not a matter of my football knowledge and it's not a personal question (that they didn't buy me) but (the problem is that) they couldn't reach their goals - they haven't been able to win promotion for years so they can't really afford to buy me.
"I have two years left from my contract so it's possible that I'll start the preparations with Debrecen. We'll see during the summer if there will be interest from other teams."