Covic, cut four weeks ago by the Sydney club which he has served with distinction since its entry into the A-Legaue in 2012-2013, revealed his management had been in talks with clubs. "Which clubs, I'm not going to say, but there are discussions going on. If there was no potential here I would be looking at something else, but my focus is still solely on playing in the A-League.
"There is definitely the potential for something to happen for me there."
Covic was speaking on the eve of his 40th birthday, on Saturday.
In a media release issued on 15 May, the Wanderers named him among a raft of players who would not be at the club next season. Covic, a foundation player at Wanderers, had been keen to continue at the club.
His non-retention at the end of a season in which he was awarded most valuable player in the AFC Champions League (ACL), a title the Wanderers won, came as a huge shock to him, but apart from saying he was disappointed in the club's decision he didn't want to dwell on that.
Instead, he is focusing firmly on the future, and his belief in his ability to continue at A-League level has not been shaken.
"I still want to play at the top level, and, not beating around the bush here, I'm far and away good enough to be at the top level," Covic said. "I've proved that and I'm not going to lower myself and say that time has now gone. I'm still up there with the best.
"Three years ago, when I left Melbourne Victory, I had people saying maybe my time was up, but quite clearly it wasn't, so I don't have to prove anyone wrong.
"I just have to prove myself right and I know what I'm capable of. There is not a question in my mind about my ability to continue playing at the top level - in the A-League or whatever it may be."
Covic is talking about playing beyond next season, as well.
"I've never looked at myself in terms of 'can I go one more year?'" he said. "I believe I can go again next year and then some. While I'm feeling good and playing well, that's always been the case. That opinion hasn't changed and at the moment it's a waiting game.
"I've left it in the hands of my agents, Nick and Bernie Mandic, to find out what's available and what the options are. I haven't looked into anything else apart from continuing to play.
"I'm confident I'll continue to play. It's just a matter of with whom, when and where - that's all still up in the air."
Covic and his wife, Linda, have two children - Emelie, eight, and Christopher, six. He said he was prepared to make the sacrifice of living away from the family home for a while to keep his playing career alive.
"Our two children are both at school, which obviously makes it a bit more tricky," he said.
"I've moved them around enough in their lives, so if it's a move out of Sydney then I'm not going to uproot them again.
"We're going to have to try to make it work where the kids have stability in Sydney and I go to do what needs to be done.
"It's a bit of a sacrifice, it's not easy, and that's another reason why it would've been great to stay in Sydney, with school-aged children. They're not so young now where you can just move them around without having to worry about school.
"I've had to do that with them once before and I don't want to do it again - they're settled.
"The main thing is what's best for the kids and I've settled here for three years and we've got a home here, so I'm not going to move the kids around. If I go somewhere, I'll go on my own and we'll make it work. We know that we can.
"I had to do that the first year after Melbourne. When I came to Sydney I came alone for a year. I have to think of what's best for the kids and I don't think the best thing at their age is ripping them out of school and going to a new place where I may not have long-term certainty or security.
"Let them have their life and friends and the school that they're used to and I'll get back home as often as I can."
Covic said that if a club offered him a spot on its roster, but with no guarantee that he would be the first-choice goalkeeper, he wouldn't be scared of the challenge.
"These are all things you have to take into consideration," he said. "I've never had a problem with pitting myself against somebody. If I was told the number one spot was up for grabs, so be it.
"I've always had the mentality that I can do a job and prove my worth and I've got no problem showing my worth to be the number one. It's not something I would whinge and moan about and say 'it's not fair'.
"When you need to fight for a position, the biggest and strongest ones always stand up and I've never been scared of a battle."
Covic said that if he couldn't finalise a deal in the A-League he would consider looking overseas - potentially in Asia.
"I'm not going to rule anything out, but at the same time I'm not going to go and do something that's out of my comfort zone or not worthwhile," he said.
"Not every move would be something I'd jump at as the right thing, but I'm not ruling anything out at this stage.
"Being a football player is a very precarious life and you have to take the good with the bad and your career doesn't last forever, so while you've still got the ambition and ability to play you have to look at every option and try to make it work."
Covic is enjoying a break after the Wanderers experienced their most hectic season in their A-League history, with two Asian Champions League campaigns squeezed in at opposite ends of the season.
"Nick and Bernie are keeping in contact with people, but on my side of things I'm just keeping it low-key at the moment," Covic said.
"When something comes up that we need to discuss they will notify me. I'd rather not sit here worrying about things and speaking to this person or that person - that's not my role. I've got people looking after that for me. My role is to play football."
