British Swimming chief executive David Sparkes claimed the bid for the event - which features swimming, diving and synchronised swimming - will help continue the momentum gained at this year's Games.
"(It) will ensure the Olympic pool has an events legacy and will allow our athletes to prepare for their next Olympic milestone, Rio de Janeiro," he said.
"A successful bid would also provide an additional legacy in terms of inspiring people within the surrounding boroughs to participate in swimming and to enjoy the health benefits this brings."
A decision about who will host the event is expected in September, and London Mayor Boris Johnson is excited about the possibility of staging the event.
"Hosting the European Swimming Championships in 2016 would see the largest event held in the Aquatics Centre after the Games and would build on the legacy of our Olympic venues as being the first choice for elite sporting events," he said.
"Swimming has a huge following in London and staging this fantastic championships would not just be a wonderful accolade for our city but a chance for Londoners to enjoy some first-class sport right on their doorstep."