As a family show, this topic has never been seriously addressed on screen. The fact the Doctor has found some of his companions attractive has been known since the original series (one of the earliest examples being when the Fourth Doctor acknowledged in dialogue that Romana I was attractive in "The Pirate Planet"). Since the series returned in 2005 hints of romance between the Doctor and his companions have occurred more frequently - sometimes subtly, sometimes not. The only companion to (so far) make undisguised sexual references vis a vis the Doctor is River Song (in, for example, "The Impossible Astronaut"), a character later established as having married the Doctor while in his Eleventh incarnation.
Otherwise, even in the modern era, the series has shied away from making direct references to the Doctor and his companions in this context. This is not considered affirmation or denial that romance may or may not have existed between, for example, Rose and the Tenth Doctor or between Clara and the Eleventh and/or Twelfth Doctors. The series writers have simply never "gone there."