It was infeasible because it was suicidal. The invasion convoys were escorted by several dozen destroyers, frigates or other escort ships with Anti Submarine weapons on board. The RAF coastal command flew numerous patrols over the English Chanel, Particularly the western approaches, near Cornwall.
Doneitz did send four U-Boats to the waters off of Normandy, but all four were sunk, without accomplishing anything, vis-a-vis the dense concentration of merchant ships the Allies had in that area.
Samuel Elliot Morrison has the complete order of battle for the US Navy, Royal Navy, Canadian Navy and Polish Navy for D-day in his book "The invasion of France and Germany 1944-1945" which is part of his fifteen volume set "History of US Naval Operations in World War II"

In addition to what /u/davratta said, the U boats were slow and unwieldy, which would lead to less effective patrol areas and lower chance of survival and attack, so fast attack craft were used more as they could cover larger areas and had a better chance of slipping away. For example, a group of nine schnellboot came across a practice landing on the coast of England about a month and a half before the Normandy landing and sank two, killing at least 638 US personnel, with no German losses.

There was so much Allied air cover that neither Schnellboats (known as E-boats to the allies) or U-boats could venture forth during the day, and German confusion about the invasion (real versus feint) kept the boats away for the first day, but they did deploy and patrol towards the Allied landing the next day. A decent overview is available on the S-boot.net site, which is perhaps a little off topic for your original question, but I suspect of interest if your are looking for German naval opposition to the landings in general.