One-time grand prix winner Martin made his MotoGP debut with Ducati as a Pramac rider in 2021 and won the Styrian GP in his rookie year.
Martin was locked in a battle with Enea Bastianini last season for a place at the factory Ducati squad, but was beaten to the seat by the four-time race winner.
The Spaniard remained on a factory contract for 2023 to stay at Pramac, but in the early part of this year, he has been linked to a potential Yamaha switch for next season.
Martin confirmed during the French Grand Prix weekend that he does have a clause in his current contract that states he can leave a year early if he is offered a factory seat.
Commenting on the rumours, Ciabatti doesn't think the Yamaha package will be good enough to entice Martin away.
"Sure he has an option in the contract, we would like him to stay with Ducati," Ciabatti told the MotoGP world feed at Le Mans.
"He's one of the fastest young riders and, at the moment, it doesn't look like Yamaha has the bike to win the championship.
"I'm sorry to say, but this is what it looks like at the moment.
"We don't know about next year, but at the moment he's on a winning bike and I think he'd like to stay because he likes to win."
Martin won the sprint race at Le Mans, marking his first victory of any kind since his Styrian GP success, and was second in the grand prix.
Yamaha's year has been incredibly difficult, with 2021 world champion Fabio Quartararo scoring the marque's only podium at the Americas GP as its championship ambitions already look remote after five rounds.
Ducati currently leads the standings with Francesco Bagnaia, one point clear of VR46 Ducati rider Marco Bezzecchi, who has won two grands prix in 2023.
But it has contested the season so far without Bastianini, who suffered a broken shoulder in the Portuguese GP sprint at the start of the campaign in March.
As such, Ducati's plans for 2024 have been put on hold, though Ciabatti doesn't think there will be any movement among its factory-contracted riders.
"Honestly, we didn't make any decisions for the future," he added.
"Unfortunately, Enea has been out for a few races, so obviously we'd like to keep all the riders with us. You know that the Gresini and VR46 riders are currently contracted to their team.
"So, the contract with Pecco, Enea, Johann [Zarco] and Jorge, in principle we're happy with all of them.
"It's a bit too early for us to say [what will happen in 2024], the problem with Enea and the crash is obviously delaying everything."
