Dovizioso's bargaining position for a fresh deal with Ducati for 2021 and beyond was strengthened considerably when the Borgo Panigale marque's top two targets, Maverick Vinales and Fabio Quartararo both re-signed with Yamaha.
Ducati was also believed to be interested in Joan Mir, but the 2019 debutant is all-but-certain to remain at Suzuki alongside Alex Rins in 2021.
But, speaking to Spanish outlet AS, Battistella claimed that Dovizioso is "open to everything" and is not "in a hurry" to land a 2021 deal.
“Ducati needs Dovizioso more than Dovizioso needs Ducati,” Battistella said. “And it's not just the need for a rider, it's the need for a technical project.
"No negotiations will begin until mid-May or the end of the month."
Dovizioso, 34 is the third-oldest rider on the MotoGP grid after Valentino Rossi and Cal Crutchlow, but Battistella insists retirement is not on his client's mind.
“Andrea wants to continue racing, of course, but at the moment he is not doing anything because he wants to see how the different projects develop,” he said.
"It doesn't bother him that Ducati has tried to recruit riders like Maverick or Quartararo, and that they are always watching what [Marc] Marquez does, just as it didn't bother him at the time if they signed [Jorge] Lorenzo or others.
“He understands that his manufacturer must [always] be looking for talented young people.”
Last year, rumours of rising tensions between Dovizioso and Ducati general manager Gigi Dall'Igna arose amid Ducati's stagnation in the competitive order.
Dovizioso's tally of two wins was his lowest since 2016, although he comfortably finished runner-up in the riders' standings behind Marquez for a third successive season.
"The most important thing for Andrea when he makes a decision is the project and the people involved," said Battistella.
"It's true that there have been tensions between Andrea and Gigi, but it's a professional tension that has helped to strengthen the project. The priority for both of them is not to impose their will [on one another], but to win, they both want to do it."