The 31-year-old Irishman, who has notched 10 goals this season, is off contract in June and the Jets are competing with Western Sydney Wanderers, Adelaide and the Mariners for his signature.
Jets football operations manager Joel Griffiths is an avowed O'Donovan fan and makes no secret of his desire to bring him to the Hunter.
"He's a player who scores goals, which is important in the A-League," he said.
"He is someone who has every right to attract the interest of other clubs and I can't see him making a decision (on his future) until after the season, and I am sure he will make the right one for him and his family.
"I think a lot of it will come down to what's best for his family ... I know the Irish are very loyal people but it will probably come down to dollars and cents at the end of the day."
O'Donovan's agent Paddy Dominguez said he had "an awful lot of options on the table and is working through them".
"That includes Central Coast, obviously," he added. "He's not in any great rush to make a decision and is flattered by the level of interest.
"That said, it may end up being a case of sooner rather than later because when you have so many clubs chasing you they want answers since they are aware of the others being interested."
While the Jets want to bring 0'Donavan in, they are resigned to losing off-contract attacking midfielder Andrew Hoole, who will head to Europe in search of a club in June.
The 23 year old wants to keep the door open at the Jets though should an offer not be forthcoming.
However Griffiths warned there were no guarantees for a player he believes is "one or two years" away from being ready to try his luck overseas.
"We are in position where we are constantly looking for players to fill the void (when he goes) and that may be unfortunate (for him) because we may already have a replacement (should he want to return)," he explained.
"I have a lot of respect for him to go over there and not have anything back here ... it's a big decision.
"He has the balls to do that and is backing himself. But if we recruit a similar player there might not be a position here for him.
"We rate him highly but I don't think he's ready yet to go overseas.
"Five goals (this season) doesn't automatically mean you're good enough to do that. I'd like to see him establish himself first.
"That's just my personal opinion and I really hope he proves me wrong.
Griffiths said his own experiences as player taught him that it takes more than just ability on the pitch to make a successful move to an overseas club.
"I know what it's like over there (from spells in England, Japan, Switzerland and China)," he said.
"You can have all the ability in the world but you have to be mentally tough.
"The A-League is a walk in the park by comparison."
While the Jets have 11 players coming off contract, Griffiths insisted that Finnish striker Aleksandr Kokko would see out the second year of his deal, despite a disappointing return of just one goal in 11 appearances.
It's believed that skipper Nigel Boogaard - understood to be among the highest paid defenders in the competition - will also see out the third year of his contract, despite murmurs the club might be be willing to let him go.
"Both players will be with us next year and I can't see that changing any time soon," added Griffiths.