The Finn, who has raced on a one-year rolling contract since joining Mercedes in 2017, was coy on the topic of his future during the fortnight in Austria.
But ahead of this weekend's Hungarian Grand Prix, Bottas said: "I can say that we have started talking about it, because yeah, I think we have all realised that time actually goes quick with these triple-headers.
"Obviously, nothing is signed yet, but I think things are moving in the right direction."
Bottas goes into the race at the Hungaroring with a six-point lead over team-mate Lewis Hamilton, who has also yet to put pen to paper on a new contract.
With his goal of finally becoming champion, Bottas added: "The main thing, as I said last weekend, is to keep focusing on the championship.
"There are big things to be achieved this year, so keep the focus on that, and I'm sure things will move on eventually.
"But of course, from a driver's side, if things drag on, it's not nice, but we've only had two races, so it's okay. There's no big panic or big rush."
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.