We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko textit{et al.} (2014). It turnsout that stability depends more strongly on the dark matter central density $%rho_{0}$ than on other parameters of the solution. This property then yields an upper limit on $rho _{0}$ for each individual galaxy, which we call here $rho _{0}^{text{upper}}$, such that stable circular orbits are possible textit{only} when the constraint $rho _{0}leq rho _{0}^{text{upper}}$ is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius $R_{text{DM}}sim 180$ kpc and find that $rho _{0}^{text{upper}}sim 2.37times 10^{11}$ $M_{odot }$kpc$^{-3}$. This limit turns out to be about four orders of magnitude larger than the latest data on central density $rho _{0}$ arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the EiBI solution could qualify as yet another viable alternative model for dark matter.
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