The 24-year-old has had his time with the Russian Premier League outfit disrupted by injuries, and is keen to end his spell in eastern Europe and return to his homeland
The Brazil international moved to the Russian Premier League from Hoffenheim back in August 2010, but has had an injury-disrupted time at the Tsentralnyi Stadion.
Having spent the last year on the sidelines due to a knee problem, the 24-year-old has admitted that he longs to go back to his homeland.
"It is positive thinking that I could go back," he is reported to have said by Globoesporte.
"Gremio are my family. My intention is to stay close to them. I travel tomorrow and I'll talk to the [Rubin board]."
After his lengthy injury lay-off, the Ajuricaba-born midfielder was keen to state that he is now fit and able to train.
"I was examined by a doctor in Germany last month. Now I can play with the ball, for real. I'm fine," he confirmed.
Eduardo is under contract at Rubin until June 2014, and the Russian side will be keen to recuperate a large chunk of the €20 million fee they paid Hoffenheim if a deal is to be done.