Which metals with high density do not react with mercury?
Here is a link to a chart of all the elements in the Periodic table and their densities.  Iridium at $22.65~\mathrm{g/cm^3}$ is the densest of all the elements with Osmium a close second at $22.61~\mathrm{g/cm^3}$.  Sigma-Aldrich sells both of these metals (Iridium \$126.50 for 0.5 gram; Osmium \$195 for 1 gram).


  the highest density material between 10 17 range that is less than
  mercury and does not react with mercury


Mercury has a density of $13.534~\mathrm{g/cm^3}$.  It sounds like you're asking for something with a density right below mercury that doesn't react with mercury. Rhodium at $12.45~\mathrm{g/cm^3}$ is probably the most readily available element with a density less than mercury.  As to rhodium's reaction with mercury, an alloy is formed at 175 C.  If you're working at room temperature, especially for shorter periods of time (like hours) you'd probably be OK, but it really depends on your specific application.