Were Mariska Hargitay and Christopher Meloni ever involved on or off the set of Law Order SVU?

Mariska Hargitay and Christopher Meloni have great on-screen chemistry in and off the set of Law Order SVU. However, they have never been involved romantically on or off the set. Christopher Meloni is married to Doris Sherman with whom he has three kids, while Mariska Hargitay is married to Peter Hermann.