The third-largest corporate transaction is estimated to be worth £80 million in fees to banks working for Verizon and £76m to Vodafone's advisers.
The Berkshire-based firm said its US stake is owned by a company in the Netherlands, making it free of UK tax liabilities.
Margaret Hodge MP, chairwoman of the Commons Public Accounts Committee, said: "Clearly there are concerns on this deal. I just want some assurance HM Revenue and Customs will be going through this deal with a toothcomb to ensure the taxpayer gets the proper benefit under the law of the tax Vodafone should pay on this massive windfall profit they are making."
She urged the Government to examine a tax exemption introduced by the last Labour administration which she said could be open to abuse.