diff --git a/src/plugins/intel_cpu/src/graph_optimizer.cpp b/src/plugins/intel_cpu/src/graph_optimizer.cpp
index d1a9e2b9db126c..7e262825e63c63 100644
--- a/src/plugins/intel_cpu/src/graph_optimizer.cpp
+++ b/src/plugins/intel_cpu/src/graph_optimizer.cpp
@@ -371,18 +371,10 @@ void GraphOptimizer::FuseFCAndWeightsDecompression(Graph &graph) {
             continue;
 
         // Precision limitations
-        if (multiplyConstNode->getOriginalOutputPrecisionAtPort(0) != Precision::FP32)
-            continue;
-        if (withPowerStatic && powerStaticNode->getOriginalOutputPrecisionAtPort(0) != Precision::FP32)
-            continue;
         if (supportedDataPrecisions.find(fcNode->getOriginalInputPrecisionAtPort(0)) == supportedDataPrecisions.end())
             continue;
         if (supportedWeightsPrecisions.find(weightsNode->getOriginalOutputPrecisionAtPort(0)) == supportedWeightsPrecisions.end())
             continue;
-        // Subtract constant can have both FP32 precision or weights precision
-        if (withSubtract && subtractConstNode->getOriginalOutputPrecisionAtPort(0) != Precision::FP32 &&
-            subtractConstNode->getOriginalOutputPrecisionAtPort(0) != weightsNode->getOriginalOutputPrecisionAtPort(0))
-            continue;
 
         // Shape limitations
         const auto weightsShape = weightsNode->getOutputShapeAtPort(0);
diff --git a/src/plugins/intel_cpu/src/transformations/transformation_pipeline.cpp b/src/plugins/intel_cpu/src/transformations/transformation_pipeline.cpp
index 3ce2669063d690..fad9321b340de9 100644
--- a/src/plugins/intel_cpu/src/transformations/transformation_pipeline.cpp
+++ b/src/plugins/intel_cpu/src/transformations/transformation_pipeline.cpp
@@ -245,7 +245,7 @@ void Transformations::PreLpt(const std::vector<ov::element::Type>& defaultPrecis
     CPU_REGISTER_PASS_COMMON(decompression_handling_manager, ov::pass::InitNodeInfo);
     CPU_REGISTER_PASS_COMMON(decompression_handling_manager, ov::pass::MarkShapeOfSubgraphs);
     // We need to fuse Transpose to MatMul to have a simpler callback for the next transformation
-    CPU_REGISTER_PASS_COMMON(decompression_handling_manager, ov::pass::TransposeMatMul);
+    CPU_REGISTER_PASS_X64(decompression_handling_manager, ov::pass::TransposeMatMul);
     ov::element::TypeVector decompression_precisions{ov::element::u8};
     // We don't have BF16/FP16 FullyConnected kernels to work with 4bits compressed weights
     // Convert node doesn't support 4bit precisions -> fallback on constant folding
@@ -254,6 +254,7 @@ void Transformations::PreLpt(const std::vector<ov::element::Type>& defaultPrecis
         decompression_precisions.push_back(ov::element::i4);
         decompression_precisions.push_back(ov::element::nf4);
     }
+    // Ticket 124834: set fold_subtract_const to false when cpu_convert supports i4/u4/nf4 precisions
     CPU_REGISTER_PASS_X64(decompression_handling_manager, ov::pass::MarkDequantizationSubgraph, decompression_precisions, true);
     CPU_SET_CALLBACK_X64(decompression_handling_manager, [&](const_node_ptr &node) -> bool {
         return !is_decompression_multiply(node);