Nighy said he wouldn't reveal when he was asked, as he felt it could bring unfair comparisons with the man who eventually got the job (i.e. Mr. Xxxxx wasn't their first choice).
I suspect he was actually up for the part of the Ninth Doctor. Remember, RTD was hoping to land a 'name', presumably to help the show get off to a strong start in the ratings and aid in international sales before they eventually went with Eccleston (who was also considered a 'name'). Also, before Eccleston was announced, Nighy was highly-touted as a favourite in the press and amongst fans.