The 31-year-old is a Los Balances stalwart having spent over a decade at the club.
However, his lengthy stint in the Spanish capital could be coming to an end.
The arrival of Ferland Mendy at the Bernabeu means the Brazil international is now further down the pecking order.
Marcelo also struggled in La Liga last term and now appears ready to pursue a fresh challenge.
“Arsenal boss Unai Emery is keen to sign Real Madrid ace Marcelo”
Spanish daily Sport say the Gunners are serious suitors, along with Juventus and AC Milan.
Arsenal are keen to sign a new left-sided defender in the coming weeks.
Kieran Tierney has been touted as a potential arrival but Celtic want top whack for their influential star.
The Scotland international is expected to cost in excess of £20m.
Marcelo, in contract, would be available for a relatively nominal sum given his advancing years.
It’s understood Emery has only around £45m to spend on fresh faces this summer.
Crystal Palace forward Wilfried Zaha is firmly on Emery’s agenda.
Arsenal reportedly tabled £40m earlier this week but had the offer rebuffed by Palace.
The south Londoners, who sold full-back Aaron Wan-Bissaka to Manchester United for £45m, want at least £80m.
Gunners legend Ray Parlour told Starsport last month that Emery must put his faith in youth.
“The club have always been run like this,” Parlour said. “The fans know exactly what happens.
“It’s another opportunity for these youngsters to get a chance.
“Reiss Nelson is one who sticks out. You’ve got Emile Smith-Rowe as well.
“I think the fans love the youngsters to get an opportunity – and that’s a road Arsenal might have to go down.
“Everybody wants big signings, but it’s got to be the right player.”
Departures are still expected from the Emirates.
Shkodran Mustafi, who has been linked with a move to Turkey, is deemed surplus to requirements.
Mohamed Elneny could also be sacrificed having failed to establish himself under Emery.