As David Hammen stated in his previous answer, neither NASA, ESA or any other space program has any extra-solar mission in the works. However, there are many studies of interstellar and interstellar precursor missions, some of them ongoing.
Perhaps the best known and most advanced interstellar probe is Project Icarus (wiki). This is a modern redesign of an earlier project from the 70s known as Project Daedelus. Icarus Interstellar is a collaborative project of the Tau Zero Foundation and the British Interplanetary Society, the latter of which came up with Daedelus. Both ship designs rely on nuclear propulsion to attain an appreciable fraction of the speed of light in order to reach a close star system within a century.
NASA produced a study on what they called the Innovative Interstellar Explorer:
This study focused on the elusive quest to reach and measure the interstellar medium, the region outside the influence of the nearest star, the Sun. It proposes to use a radioisotope thermal generator with ion thrusters.(1) The project is a study of a proposed interstellar precursor mission that would probe the nearby interstellar medium and measure the properties of magnetic fields and cosmic rays and their effects on a craft leaving the Solar System.(2)
Using an ion drive with xenon propellant, it could attain 1000 AU within 100 years of launch (updates here and here, slide show here).
Another interstellar precursor probe is Project FOCAL, a proposal by Italian physicist Claudio Maccone. The idea is to send a probe out to 550 AU and beyond in order to use the Sun as a gravitational lens.
I would be remiss if I did not mention the 100 Year Starship Project, headed by American physician and former NASA astronaut Mae Jemison. This is a DARPA sponsored project to come up with a business plan for research on interstellar travel over the next hundred years.