Antonis, who scored the Sky Blues’ winner in Saturday’s rip-roaring derby against Western Sydney Wanderers, nearly joined Parma 17 months ago for $300,000.
However, the deal fell through after he suffered a long-term quadriceps injury.
Last November, he signed a new two-year extension which will keep him at Moore Park until mid-2017.
Though flattered to have overseas suitors knocking on the door again, he remains focused on playing his part in Sydney’s push for a top-two A-League finish.
Antonis, who came off the bench to fire Sydney’s clincher in its dramatic 4-3 victory at Pirtek Stadium, said: "I am really happy at Sydney, it's the club that has always done the right thing by me and helped me develop and learn.
"(Coach) Graham Arnold has taught me a lot of new aspects to my game which I am working on and we believe we can push on now and keep the pressure on at the top of the table.
"I’m not looking too far ahead but of course every player wants to test themselves at the highest level they can reach and I am no different.
"There was of course the interest from Italy in the past and if anything cropped up again then you’d have to look at it, but it’s not something I am giving any real thought to right now.
"We have a lot to play for this season and I want to be a big part of that."
It's believed the Sky Blues would not seriously entertain any offers below $800,000 for their young gun.
Antonis, 21, has not been a regular starter for the Sky Blues since returning from AFC Asian Cup duty for the Socceroos, coming off the bench in three of Sydney’s past four games with the club picking up 10 points from a possible 12 in the process.
But he is not making any waves, fully aware of the depth of the Sky Blues squad and is backing his own ability to force his way back into the first XI as fifth-placed Sydney enters the home straight of the regular season, just four points adrift of leader Perth Glory.
The first of its eight games before the finals comes against the lowly Newcastle Jets at Hunter Stadium on Friday night, with Antonis adding: "I think the win against Western Sydney showed the character in this side.
"When you lose a three goal lead there's always the chance the wheels can fall off but we hung in there and fortunately I was in the right place to score the winner.
"We’re a team which never gives up, no matter what the situation and that’s going to stand us in good stead for the rest of the season."
Antonis gets his chance to cement his starting spot again against the Jets with Senegalese midfielder Mickael Tavares banned for one match after his red card against the Wanderers.
Sydney FC CEO Tony Pignata said he was unaware of any new interest in Antonis, declaring: "I have heard nothing for now and we are happy with Terry.
"He has come back from Asian Cup and Graham Arnold has slowly re-introduced him and he made a big impact when he came on against the Wanderers.
"It's been a question of Arnie nursing him back in after four weeks without playing."
Sydney has yet to reveal its hand on whether it will seek to secure marquee striker and Golden Boot front-runner Marc Janko for another season after he took his tally to 12 with a double at Pirtek Stadium.
With the club understood to be unwilling to match the $1.4 million he signed on for in 2014-2015, Pignata said: "Nothing has changed (regarding potential talks over a new deal) but there's no doubt he's a quality player."
