Several petitions were filed in 2014 and 2015 after the then Congress-NCP government granted 16 per cent quota in government jobs and education to the Maratha community.
In November 2014, in an interim order, a division bench of the Bombay HC had stayed the then government's decision.
While some of the petitions opposed the government's decision, two petitions had sought immediate implementation of the quota.
Vinod Patil, one of the petitioners, mentioned the matter Monday before a division bench headed by Justice BP Dharmadhikari, seeking an urgent hearing.
Justice Dharmadhikari said he will hear the petitions on Wednesday.
The Maratha community had held protests across the state earlier this year demanding quota in jobs and educational institutions.
On Sunday, the Maharashtra government approved reservation in government jobs and educational institutes for members of the community.
The state's approval followed the recommendations by the State Backward Class Commission.
While hearing Patil's petition, the court had, however, in August this year directed the commission to submit a report on the progress in its research on whether the community deserved such reservation.
Patil has now sought that the commission's recommendations made to the state be submitted before the court.
He has also urged the court to direct the state to implement the quota for the Maratha community in a time-bound manner.