The 29-year-old former Pohang Steelers frontman left the Riverside on Tuesday after failing to hold down a regular first-team place following his move to England in January 2007.
Lee was not named in Huh Jung-moo's squad for the forthcoming World Cup qualifier against Jordan as he is unavailable due to the ban he received following an incident at the Asian Cup.
"We cannot disclose all the teams under negotiation, but we plan to make our choice within the next three months," Lee's agent Kim Ki-Hoon told Yonhap news agency.
"We believe we have no need to hurry, although we hope for the earliest deal possible."
Lee, who previously played for K-League outfit Gwangju Sangmu Phoenix and also had a six-month loan spell at Werder Bremen, scored twice in 29 appearances for Boro but did not feature after February.
"I will join a club where I'm wanted and I can be of help," said Lee. "I'll take my time to weigh up my decision."