Hamilton's current Mercedes deal runs out at the end of this season, prompting traditional speculation on whether the 38-year-old will re-commit to the team that propelled him to six of his seven world championships or walk away from the series.
It even prompted wild speculation about a possible move to Ferrari, which was quickly refuted by all parties.
Both Hamilton and Wolff have regularly suggested they could thrash out a fresh deal without great difficulties, and after Sunday's Spanish Grand Prix, Hamilton gave the firmest hint yet that a contract extension is imminent.
When asked in the post-race press conference if a new deal is in the pipeline, Hamilton chuckled: "Well, I haven't signed anything yet, but we I think we're going to meet with Toto tomorrow. So hopefully, we can get something done."
Hamilton's words were echoed by Wolff when he was asked by Sky Sports F1 when Hamilton's new deal would be concluded.
"I think we just need to get time to sit over coffee. That's going to take half an hour," he said.
Hamilton felt his Mercedes contract situation has no bearing on his performance but admitted that it would be easier for him and the team to focus on challenging Red Bull in 2024 once the deal is out of the way.
"Well, you can see today: my results, my performance is not affected by that," Hamilton explained.
"I think it's always something that's at the back of your mind, so once this is done, then you're able to then focus more about the future.
"But as I said, I'm working as hard as I can with this team. And I see so much strength within a team, I think they are still so hungry.
"The podium today was really, really special; to be able to see the excitement in all the people that I've worked with such a little time.
"When we go back right now, there'll be great energy within the office. But these guys just don't take two seconds to enjoy themselves and be happy.
"And then they'll be back down into the books, trying to figure out how we can win the next race. That's what I love about them."
