I heard that they will be building a shopping center near your home.
I heard that they will be building a shopping center near your hoouse.
I heard that they will be building a shopping center near where you live.
I heard that they will be building a shopping center near your home.
「あなたのお住まいの近くに」と表現するにはnear your home/ house. where you liveを入れたほうが具体性があり理解しやすいと思います。
near thereですと、すでに会話の中で特定のエリアの話をしていないと、thereがどこをさすのかわからず混乱させてしまうためです。