The South Korean striker has failed to find the net in the Premier League since joining the Teesside team in January 2007.
Boro boss Gareth Southgate admitted last week that Lee is unlikely to play for the rest of the season.
"I think it's difficult for him to have any sort of a chance. For him and for the team I think it's been better to involve other players really," Southgate said.
The 29 year-old forward is keen to stay in Europe and is not about to return to old club Pohang Steelers.
"Recently I spoke to Lee Dong-guk because there have been lots of rumours flying around," a source close to Pohang told Sports Seoul.
"He tried so hard to get where he is and he said he will definitely not return to the K-League."