"Aceiași aleargă cu mine."

I think in English you would usually add a noun to specify: the same PEOPLE/GUYS/FRIENDS, etc. Or, if previously specified (context), you might say "the same ONES". I just suggested this version be accepted as a correct answer.

I suppose this it the direct translation but we would never say this in English. We might say, "They are running with me", or "These are running with me".