Leveraging an offer

Good evening everyone.

Bottom line up front:  how do I leverage an offer from another firm to get a raise at my current firm?  

Details:  I may get an offer soon from another firm but there is a chance it will not be sufficient to be a meaningful increase in income due to a higher cost of living and higher benefit costs at the new firm.  So the offer may not be one I want to take (of course it may be and this is a moot point). But it would be nice if my current company would give me some sort of counter offer of a pay increase connected to this offer. How do I throw out the idea I would entertain a counter offer without committing to the new firm?  I don’t want to be unprofessional but of course a pay increase would be welcome.

Thank you!

John