If @RealDonaldTrump wants to add another obstruction of justice charge by firing Rosenstein, he'll have to do so. Rosenstein isn't resigning and has not offered to do so.
Rod Rosenstein ("source close to" means this) is not resigning, and has not offered to resign.
Trump may obstruct justice by firing Rosenstein, he must really long for that jail cell, but Rosenstein is not resigning.
It doesn't depend on individuals.