Moukoko's deal with the Signal Iduna Park outfit expires at the end of this season and Dortmund have presented him with fresh terms.
Moukoko is yet to put pen-to-paper and is generating interest from some of Europe's leading clubs.
The 18-year-old has scored six goals and provided three assists in 14 Bundesliga appearances this season.
Dortmund's sporting director Sebastian Kehl has given Moukoko and his entourage up until the Bundesliga resumes this weekend to make up their mind.
Speaking to Kicker Magazine, Kehl said: "We have put together a very attractive offer that gives him a lot of room for development. That should lead to a decision. He has to make it with his environment and his advisor.
"Youssoufa can now accept this offer and commit to Borussia Dortmund, or we will go our separate ways. I would like him to choose us because he is not yet at the end of his development and I see huge potential in him. But there are limits for us as a club. And we have shown these limits. Now it's up to him to decide.
“Youssoufa and his advisors know that we are expecting a decision this week because we want to have this clarified before the first game back [after the World Cup break] so that the boy can devote himself entirely to the sporting challenges."
"Youssoufa is a great boy," he added. "He's been with us for almost seven years, we trained and developed him. He became a professional and a national player with us. He received an incredible amount of support from us and worked hard to achieve success himself."
