Assuming, as neilfws suggests, that you are interested in finding orthologues, you can use NCBI's HomoloGene DB.
This file (ftp://ftp.ncbi.nih.gov/pub/HomoloGene/current/homologene.data) contains the mappings you need. Col2 is taxonomy ID, col3 is Entrez Gene ID.
You can also provide a list of Entrez IDs in Ensembl Biomart and get mapping from the corresponding Human Ensembl gene to the orthologous Mouse Ensembl gene. See here for an example using two Human Entrez Gene IDs (You may need to click the 'Results' button, if it doesn't load automatically). Those Ensembl identifiers can then also easily be mapped back to Entrez IDs using Biomart. Not sure if it can all be done in one query. See here for an explanation of how homology is determined by Ensembl.