There have been reports of possible detections of intermediate-mass black holes (IMBHs) in globular clusters (GCs). Empirically, there exists a tight correlation between the central supermassive black hole (SMBH) mass and the mean velocity dispersion of elliptical galaxies, ‘pseudo-bulges’ and classical bulges of spiral galaxies. We explore such a possible correlation for IMBHs in spherical GCs. In our model of self-similar general polytropic quasi-static dynamic evolution of GCs, a heuristic criterion of forming an IMBH is proposed. The key result is , where MBH is the IMBH mass, σ is the GC mean stellar velocity dispersion, is a coefficient and 2/3 < n < 1. Available observations are examined.