Lee returned to Japan in February but has rejected the chance of a permanent move because he felt he was not getting enough time on the pitch.
The 27-year-old started just four games, coming off the bench on nine other occasions, but did score four goals during his loan spell in Tokyo.
Lee said: "I felt like I was only playing in fits and starts and thought a different challenge would be better for me.
"Maybe it was a case of me not being good enough. I spoke to the coach and we tried to work something out."
Lee, who joined Saints from Sanfrecce Hiroshima in January 2012, is not thought to feature in the long-term plans of manager Mauricio Pochettino.