diff --git a/easybuild/easyblocks/s/superlu.py b/easybuild/easyblocks/s/superlu.py
index f44c9bcb39b..40042409aca 100644
--- a/easybuild/easyblocks/s/superlu.py
+++ b/easybuild/easyblocks/s/superlu.py
@@ -26,6 +26,7 @@
 EasyBuild support for building and installing the SuperLU library, implemented as an easyblock
 
 @author: Xavier Besseron (University of Luxembourg)
+@author: J. Sassmannshausen (ICL/UK)
 """
 
 import os
@@ -61,7 +62,12 @@ def configure_step(self):
         Set the CMake options for SuperLU
         """
         # Make sure not to build the slow BLAS library included in the package
-        self.cfg.update('configopts', '-Denable_blaslib=OFF')
+        # At least for version 5.3.0 the name has changed:
+        superlu_version = self.version
+        if LooseVersion(superlu_version) >= LooseVersion('5.3'):
+            self.cfg.update('configopts', '-Denable_internal_blaslib=OFF')
+        else:
+            self.cfg.update('configopts', '-Denable_blaslib=OFF')
 
         # Set the BLAS library to use
         # For this, use the BLA_VENDOR option from the FindBLAS module of CMake
@@ -72,6 +78,7 @@ def configure_step(self):
             raise EasyBuildError("No BLAS library found in the toolchain")
 
         toolchain_blas = toolchain_blas_list[0]
+        cmake_version = get_software_version('cmake')
         if toolchain_blas == 'imkl':
             imkl_version = get_software_version('imkl')
             if LooseVersion(imkl_version) >= LooseVersion('10'):
@@ -88,10 +95,24 @@ def configure_step(self):
             self.cfg.update('configopts', '-DBLA_VENDOR="%s"' % toolchain_blas)
 
         elif toolchain_blas == 'OpenBLAS':
-            # Unfortunately, OpenBLAS is not recognized by FindBLAS from CMake,
-            # we have to specify the OpenBLAS library manually
-            openblas_lib = os.path.join(get_software_root('OpenBLAS'), get_software_libdir('OpenBLAS'), "libopenblas.a")
-            self.cfg.update('configopts', '-DBLAS_LIBRARIES="%s;-pthread"' % openblas_lib)
+            if LooseVersion(cmake_version) >= LooseVersion('3.6'):
+                self.cfg.update('configopts', '-DBLA_VENDOR="%s"' % toolchain_blas)
+            else:
+                # Unfortunately, OpenBLAS is not recognized by FindBLAS from CMake,
+                # we have to specify the OpenBLAS library manually
+                openblas_lib = os.path.join(get_software_root('OpenBLAS'), get_software_libdir('OpenBLAS'),
+                                            "libopenblas.a")
+                self.cfg.update('configopts', '-DBLAS_LIBRARIES="%s;pthread"' % openblas_lib)
+
+        elif toolchain_blas == 'FlexiBLAS':
+            if LooseVersion(cmake_version) >= LooseVersion('3.19'):
+                self.cfg.update('configopts', '-DBLA_VENDOR="%s"' % toolchain_blas)
+            else:
+                # Unfortunately, FlexiBLAS is not recognized by FindBLAS from CMake,
+                # we have to specify the FlexiBLAS library manually
+                flexiblas_lib = os.path.join(get_software_root('FlexiBLAS'), get_software_libdir('FlexiBLAS'),
+                                             "libflexiblas.so")
+                self.cfg.update('configopts', '-DBLAS_LIBRARIES="%s;pthread"' % flexiblas_lib)
 
         else:
             # This BLAS library is not supported yet