As @mwaskom commented, I was able to use it ax_heatmap.set_position
along with the function get_position
to achieve the correct result.
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
np.random.seed(2)
data = np.random.randn(100, 10)
cm = sns.clustermap(data)
hm = cm.ax_heatmap.get_position()
plt.setp(cm.ax_heatmap.yaxis.get_majorticklabels(), fontsize=6)
cm.ax_heatmap.set_position([hm.x0, hm.y0, hm.width*0.25, hm.height])
col = cm.ax_col_dendrogram.get_position()
cm.ax_col_dendrogram.set_position([col.x0, col.y0, col.width*0.25, col.height*0.5])

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