The Australian has been linked with potential moves to Ferrari, Mercedes or even McLaren or Renault.
Yet now that Red Bull's Honda engine deal is in place, team consultant Marko said efforts that are now moving onto getting Ricciardo's signature on a page.
However, he admitted that the Honda deal is not quite finalised.
"A few details must be fine-tuned," he told Speed Week.
"But we have had a close relationship with Toro Rosso and Honda.
"For the first time we are becoming a factory team. And in resources and methodology, we recognise Honda as the most promising option. We can go for victories with Honda in 2019."
Marko said that a new deal with Ricciardo is then the next step.
"We've had more discussions recently," the Austrian revealed.
"We're getting closer to each other. To speak in Mercedes jargon, it's just about the details."
There is also more potential for the rest of the season with Renault, Marko insisted.
"On Saturday we will get the stronger mode for qualifying, which was promised since Canada," he said.
"But we don't know how much stronger it will be and how much we will catch up with Mercedes and Ferrari who have always had the party mode."
Red Bull trail second-placed Ferrari by 50 points going into Sunday's Austrian Grand Prix.