Whether you choose an international bank or a UAE-based bank, your presence is mandatory. Most, if not all, banks require physical verification of the applicant’s identity.
However, some major online banks such as Bank of Internet USA and Charles Schwab Bank, allow one to open an account online on the basis that the person wishes to remain a citizen of his/her home country. The downside of opening an online account with web-based financial institutions is that your account will be based locally with no access to on-site customer service and tellers. Your transactions, such as cheques might take longer to get approved. However, you will enjoy some privileges such as flat currency conversion rates and free ATM withdrawals.
The same applies to most major international banks operating in Dubai. For example, Citibank allows you to open an account online in Dubai provided you have a residency and an address in the U.S. With HSBC, you can also apply either from the UK or the UAE. Both HSBC and Citibank offer waivered ATM fees and access to on-site bank tellers in Dubai for online accounts.