Chronic Lymphocytic Leukemia (CLL) is among the cancers with the highest incidence and mortality in Mexico according to Globocan 2020. The most common cause of this type of leukemias is abnormalities in hematopoietic stem cells which are precursors to leukocytes (i.e. deletions, translocations, or additional chromosomes). In CLL, the mutations primarily affect B lymphocytes, where macrophages derived from monocytes promote the proliferation of cancerous cells. In addition, some experimentally grounded Gene Regulatory Networks (GRNs) models have started to be proposed to uncover the CLL regulatory core, thus contributing to the understanding of the emergence of complex patterns involved in the dynamics of cancer tumor progression. Nevertheless, systematic analyses that elucidate the specific role of the involved genes (acquired by their collaboration in the network) are still very scarce. In this work, we propose both AI-based algorithm and bifurcation approach, to classify and analyze the qualitative behavior of the stable states corresponding to the M0, M1, M2 and NCL phenotypes in the underlying of macrophage polarization in CLL-GRN. Furthermore, the dynamic transitions between these phenotypes are analyzed and related through the variation of exponential decay rates in genetic expression. Finally, the biological relevance is discussed with previously reported experimental evidence.