Middlesbrough chief confident of Downing agreement
However, Lamb is confident that the situation could be resolved soon.
Speaking at a BBC Radio Tees fans' forum, he said: "I am very confident that we will reach agreement sooner rather than later.
"It is something that myself and Steve Gibson have been very conscious of and have been working at over the last couple of weeks.
"I would not like to put a date on it, but I would hope that within the next four to six weeks, we get a solution to it that's acceptable to Stewart and to the football club, and then we can put it to bed and Stewart can concentrate on playing his football."