The 27-year-old striker was released by Bundesliga side Schalke at the end of last season, and is keen to continue his career in the Premier League.
Gunners boss Arsene Wenger has been offered the Romania international's services, as he looks to strengthen his attacking ranks at the Emirates Stadium ahead of the 2013/14 campaign, which kicks off in less than two weeks time.
Marica's agent, Giovani Becali, confirmed that his client is in advanced talks with the north London club, and hopes a decision will be made in the next few days.
"He is close to Arsenal, we'll see this week," said Becali. "Marica is a very good striker, a Romanian national player who has great experience."
Marica would be the second free agent that Arsenal have signed this transfer window, in what has been a frustrating summer for the club, having missed out on a number of high-profile targets already.
Yaya Sanogo arrived from Auxerre on a free transfer, but is the only new arrival so far, since the end of the 2012/13 campaign.
In addition to Sanogo and Marica, Arsenal are also giving trials to two midfielders, Atletico Nacional's Sebastian Perez, 20, and 26-year-old Angers star Alharbi El Jadeyaoui.