I am a US based consultant who started subcontracting consultants abroad. I will start making payments to one of them who is living in another country but has an US bank account. I wonder if there is any tax liability for me if the contractor does not pay taxes.

Is the payment for services or for some other type of transaction?

If you are making payment for services to a foreign alien, the income of the foreign alien is not taxable in the U.S. You do not need to withhold any taxes. Get W8-BEN from the foreign sub-contractor.

The payment is for services. Thank you

Agreed; no U.S. taxes are due.

You MAY want to check if there is a requirement to submit a tax report to the tax ministry of the sub-contractor's home country.