The 27-year-old, who has spent eight years in England, is currently without a club after leaving Luton at the end of last season.
Kovacs has confirmed that he has an offer from an unnamed Scottish club, but concedes that he wants to return to Hungary for personal reasons.
He told Nemzeti Sport: "I've already confirmed that a team from the Scottish top flight are interested in me. I'm fortunate that there have been further offers since then.
"It is true that I have spent most of my career in England - the atmosphere is wonderful but now I feel like I would like to play in Hungary, if possible.
"I want to go home because of my family, my friends and also because I like what has happened in Hungarian football over the last few years."
He is currently training with Hungarian champions Gyori ETO FC.