Noninvasive early detection of liver cirrhosis and fibrosis is essential for management and therapy. The aim was to investigated whether a combination of the functional parameter relative enhancement (RE) on Gadoxetic Acid magnetic resonance imaging (Gd-EOB-DTPA-enhanced MRI) and the fibrosis parameter T1ρ distinguishes cirrhosis and healthy liver. We analyzed patients with Gd-EOB-DTPA-enhanced MRI and T1ρ mapping. Signal intensity was measured before and after contrast; RE was calculated. T1ρ was measured with circular regions of interest (T1ρ-cROI). A quotient of RE and T1ρ-cROI was calculated: the fibrosis function quotient (FFQ). Cirrhosis was evaluated based on morphology and secondary changes. 213 datasets were included. The difference between cirrhotic and noncirrhotic liver was 51.11 ms vs. 47.56 ms for T1ρ-cROI (p < 0.001), 0.59 vs. 0.70 for RE (p < 0.001), and 89.53 vs. 70.83 for FFQ (p < 0.001). T1ρ-cROI correlated with RE, r = -0.14 (p < 0.05). RE had an AUC of 0.73. The largest AUC had the FFQ with 0.79. The best cutoff value was 48.34 ms for T1ρ-cROI, 0.70 for RE and 78.59 ms for FFQ. In conclusion T1ρ and RE can distinguish between cirrhotic and noncirrhotic liver. The FFQ, which is the combination of the two, improves diagnostic performance.