The Slovenian striker only linked up with the Bluebirds last summer, but has grown disillusioned with life in South Wales after just 12 months.
An inability to force his way into Malky Mackay's plans has left him kicking his heels on the sidelines.
Promotion to the Premier League is unlikely to have helped his cause, with competition for places having increased.
Velikonja concedes that it is now time for him to look for a fresh start, and he hopes Cardiff will be understanding of his situation and make themselves open to any further offers.
He told Nogomania: "I want to move somewhere where I will be able to play, as I surely won't get any chances at Cardiff.
"I had an offer from Portugal, but the club said no. I don't know why.
"I also don't know why I'm not playing at all. I don't believe the problem is me. I would really like to play. To get a chance at least."