The Grove-based team confirmed at the start of December that Pastor Maldonado would be retained for 2012 but there is still no word on a team-mate for the Venezuelan.
Adrian Sutil, who was released by Force India late last year, seemed the favourite but the German's hopes of finding a seat have received a major setback with the news that he is to stand trial for an alleged nightclub assault.
Bruno Senna is now being strongly linked with Williams but Barrichello is not giving up hope that he will be retained for what would be a 20th F1 season.
"It's taking longer than I wished for, to be honest," the 39-year-old Brazilian told Peter Windsor's The Flying Lap.
"I have been thinking positively, (and) have always put it this way: you've got to believe in things and, if they haven't happened just yet, you have got to believe that they have happened in your mind.
"I am fighting for the position. I think there are two other drivers who have potential to be driving at Williams, but I feel like I am quite a good candidate and that I should be driving there."
Williams endured the worst season in their history last year, finishing ninth in the contructors' championship with just five points.
However, they have undergone a shake-up of their technical team ahead of the new season with, for example, Mike Coughlan brought in as technical director.
The renewal of Williams' association with Renault - which brought them five world titles in the 1990s - offers further proof of a team looking to turn over a new leaf, with Barrichello certain his experience can make a difference.
"There's lot of changes for the team - the engine, new people around - and I think what I can tell people at Williams is that experience comes gratis, in a way. It's just there," Barrichello, who has started a record 322 grands prix, added.
"Where are you going to find someone with my experience and so much of a will to do well? I still have so much feeling for the car and I want to drive it as fast as I can.
"I don't know how that is happening because, when I was in my 20s, I thought 'I don't know, maybe when I'm 30, I'm done'.
"I'm now 39 and I'm still feeling ready to go. I think this is the best thing that can be happening to me right now and I hope to be driving this year."