Albumin is synthesized by:
Quick Review of plasma proteins

Most abundant plasma protein-Albumin
Least abundant plasma protein-Alpha-1 Globulin
Plasma protein with fastest electrophoretic mobility-prealbumin (Transthyetin) followed by albumin. Plasma protein with least electrophoretic mobility-Gamma Globulin
Most plasma proteins are synthesized in the liver except immunoglobulins by plasma cells of B Lymphocyte lineage
Most Plasma proteins are Glycoproteins except Albumin, which is a simple protein. Many plasma proteins exhibit polymorphism.

They are:

α1-antitrypsin
Haptoglobin
Transferrin
Ceruloplasmin
Immunoglobulins.

Key concept:
Like most of the plasma proteins albumin is also synthesised in liver.
Liver
Kidney
Muscle
Spleen