The Brazilian outfit have admitted that they would like to bring the midfielder to the club but have hit a stumbling block in the valuation of the 26-year-old star
The former Fluminese playmaker has struggled to hold down a regular place in the Stadio Olimpico outfit's starting 11 and Gremio want to offer him a route back to his native Brazil.
The club's president Fabio Koff revealed that they have spoken to the player and are hoping to bring him to South America before the end of their transfer window.
"We will not give up on getting Marquinho," he told Radio Bandeirantes.
"There have been some problems with Roma's valuation.
"But we have made a proposal to the player, and we hope that he agrees to come, because the market in Brazil is still open."
The 26-year-old only signed permanently for Giallorossi in the summer after impressing in a loan spell towards the end of the 2011/12 season.