Drogba has been reported to be seeking a move to Italy after a season fraught with rumours of wage disputes at Shanghai Shenhua and failure to settle into China.
The Ivorian striker has a release clause with the Chinese club and has been recently linked with a January move to either AC Milan or Juventus.
Marotta confirmed the Bianconeri's interest in Drogba and believes that the 34 year old will be a huge boost for the club's Champions League prospects.
"You always explore your options and that's what we have done regarding Drogba. We have noted his availability," he told Domenica Sportiva.
"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."