As the incidence of small-diameter vascular graft (SDVG) occlusion is considerably high, a great amount of research is focused on constructing a more biocompatible graft. The absence of a biocompatible surface in the lumen of the engineered grafts that can support confluent lining with endothelial cells (ECs) can cause thrombosis and graft failure. Blood clot formation is mainly because of the lack of an integrated endothelium. The most effective approach to combat this problem would be using natural extracellular matrix constituents as a mimic of endothelial basement membrane along with applying anticoagulant agents to provide local antithrombotic effects. In this study, we fabricated aligned and random electrospun poly-L-lactic acid (PLLA) scaffolds containing acetylsalicylic acid (ASA) as the anticoagulation agent and surface coated them with amniotic membrane (AM) lysate. Vascular scaffolds were structurally and mechanically characterized and assessed for cyto- and hemocompatibility and their ability to support endothelial differentiation was examined. All the scaffolds showed appropriate tensile strength as expected for vascular grafts. Lack of cytotoxicity, cellular attachment, growth, and infiltration were proved using 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay and scanning electron microscopy. The blood compatibilities of different scaffolds examined by in vitro hemolysis and blood coagulation assays elucidated the excellent hemocompatibility of our novel AM-coated ASA-loaded nanofibers. Drug-loaded scaffolds showed a sustained release profile of ASA in 7 days. AM-coated electrospun PLLA fibers showed enhanced cytocompatibility for human umbilical vein ECs, making a confluent endothelial-like lining. In addition, AM lysate-coated ASA-PLLA-aligned scaffold proved to support endothelial differentiation of Wharton's jelly-derived mesenchymal stem cells. Our results together indicated that AM lysate-coated ASA releasing scaffolds have promising potentials for development of a biocompatible SDVG.