The Chelsea legend, who has reportedly failed to settle in China, is set to return to Europe just six months after leaving London to join Shenhua on a lucrative deal.
Drogba is reported to have an option to end his two-and-a-half year contract early and has been linked with Italian giants Juve and AC Milan.
Marotta confirmed Juve's interest when he told Domenica Sportiva: "You always explore your options and that's what we have done regarding Drogba. We have noted his availability,"
"We will now find out whether his financial demands are compatible with what we can offer. After that the matter will be further discussed with the coach.
"It's only normal that a club like Juventus are looking to strengthen as we want to win the Champions League again. It's not easy to find a solution that makes sense financially, too."
The 34-year-old striker is currently preparing for the Africa Cup of Nations with Cote d'Ivoire.