Fulop spent four years at the Stadium of Light before moving on to Ipswich, West Brom and then to Greece with Super League club Asteras Tripoli.
His contract there came to an end at the end of the season and the Hungarian now intends to focus on making a full recovery.
Fulop told Sunderland's official website: "I am sure that, after a few months,
I will be ready both physically and mentally to continue playing football.
"What is more, I'd like to train between the treatment courses, as the doctors have said this is fine, and in fact, they heartily recommend it.
"I am very grateful to all the messages and good wishes - it really helps me that many are thinking of me."