Ricciardo has been with Red Bull since joining sister team Toro Rosso as a test driver in 2011.
The Australian made his debut for the senior team in 2014 and has since amassed 786 F1 World Drivers’ Championship points and five Grand Prix victories.
The 28-year-old remains one of the highest-rated drivers on the grid and has attracted interest from Mercedes and Ferrari by not signing a new deal with Red Bull.
His current contract ends in less than 12 months’ time and while Horner is not in a massive hurry to do the deal, he would like to wrap it up well before the new season begins on March 25.
“We’ve just come through a long hard season, so the last thing we’re going to be doing is getting into the depths of contract discussions,” Horner told Sky Sports.
“But I think early in the new year, once we’ve seen how the car’s performing, how things are panning out, then it’s our priority to make sure that we retain Daniel in the team until at least 2020.”
Ricciardo’s team-mate Max Verstappen signed a new three-year deal in October to end speculation linking him with a move up the grid.
However, the Dutchman stressed that he only did so because he expects to be challenging at the front of the grid: the 20-year-old was only able to pick up two race wins in 2017.
Ricciardo too is keen to be challenging Ferrari and Mercedes in the Drivers’ and Constructors’ Championships, but at 28 has less time to waste on the reliability issues experienced in 2017 by Red Bull.
The Milton Keynes-based outfit suffered a total of 13 retirements in 20 races in 2017, leaving the Australian deeply frustrated on multiple occasions.
But if he does end up leaving Red Bull as a free agent at the end of 2018, Horner insists the team will have no shortage of replacements lined up.
Horner added: “We’ve invested a lot in the young driver programme over the years and we’ve got some great talent on the programme.
“We’re certainly not short of options.”