The 24-year-old - who has made 180 league appearances for the Riverside Stadium outfit - has long been linked with a move to White Hart Lane, who attempted to sign the England international during the winter transfer window.
The Teeside club are still anticipating Downing's exit this summer following their relegation to the Championship, despite the winger being sidelined for several months with a foot injury sustained at the end of last season.
And Lamb has revealed that Boro would be willing to listen to any approach from Spurs, should they wish to renew their interest in the player, who has played 23 times for his country.
"I wouldn't rule anyone out and anyone in. Stewart's sale is not vital," he said.
"Spurs might find it difficult to re-open negotiations on Stewart and it wouldn't be the easiest negotiations from their point of view.
"But I would certainly take their call.
"We are disappointed he is injured because it is important he gets back to playing football as quickly as possible.
"It could be between four and six months and Stewart believes he will be back sooner rather than later."
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