The Mariners are close to making an offer for the 31-year-old Spaniard, who was released by Victory at the end of the season in what was widely regarded as a surprise decision.
Central Coast CEO Shaun Mielekemp told The World Game it was important the club move quickly on the players they want to sign for next season.
"I'm sure every A-League club that have positions to fill would look at Alan Baro, he's a fantastic player," Mielekamp said.
"It's a competitive market out there for players and often it's first in, best dressed, so, yeah, he's on our shopping list.
"We've had talks with Baro's management and we're just working through the process to make sure if we do table an offer it's the best one we possibly can, so we don't miss that opportunity."
Baro, in his first year in the A-League, improved as he got more used to the competition and was particularly effective towards the end of the season. He was among Victory's best players in their grand final loss to Sydney FC.
But the Victory had signed Australian central defender Rhys Williams from Perth Glory and are understood to have made attacking players a priority to fill remaining visa spots.
The Mariners would have no trouble making space for Baro, because after their recent decisions on player retention they have all five visa spots available.
Mielekamp said the club had to use that opportunity to advantage.
"The priority for us is visa players and when Paulo (coach Paul Okon) came back from his recent trip overseas he had his eye on some key targets and we're working through the list of those players now," Mielekamp said.
"We hope to have some of those new players signed in the next couple of weeks."
Asked if Baro could be among those players signed soon, Mielekamp said: "We're in a good position at the moment with key spots available, so we've just to be very smart about what we do and take advantage. Hopefully, things will fall well for us in that space - the next two weeks is crucial for us."
Newcastle Jets are also a potential new home for Baro, but they have only two visa spots available and one of those must go to a Chinese player. The club's new coach, Ernie Merrick, may favour an attacking player to fill the other spot.
Adelaide United are another club in need of a central defender, with Dylan McGowan having left, but they are delaying decisions on visa spots until they appoint a new coach.
Mielekamp confirmed attacker Sergio Cirio, released by Adelaide, was another player the Mariners were looking at closely, along with overseas targets.
"There's a Dutch defensive midfielder we've got an offer in for and we're hoping things fall into place there in the next seven to ten days," he said. "There are good times ahead for our recruitment."