Everton are on the search for defenders in the January transfer window.
Martinez has good links with the Spanish giants and he is hoping to utilise them again in the new-year to help strengthen his side's defence.
Everton have struggled with persistent injury problems to their backline throughout the season so far and Martinez is determined to bring in more numbers at the next available opportunity, as a result.
Douglas is apparently one of his targets, as the Brazilian has struggled to force his way into the team at the Nou Camp.
The 24-year-old signed for the Catalan club this summer from Sao Paolo, but he has made just one league appearance and the thought is that Barcelona could be open to allowing him to leave on a temporary move to regain some match sharpness.
Everton took Gerard Deulofeu on loan last season and aided his development, meaning that Barcelona have faith that their fringe players can benefit from a move to Goodison Park.
Douglas is renowned for his attacking instincts and pace, making him the sort of full-back perfectly suited to play in Martinez's fluid system.
Tony Hibbert has regularly been utilised at right-back so far this season but, despite his experience, there are question marks over his ability and Douglas would unquestionably be an upgrade.
Everton have also been linked with West Ham United centre-back Winston Reid in recent weeks.