"I'd be amazed if he left," Horner told reporters ahead of Sunday's British Grand Prix.
"I would think he's got (Mercedes team boss) Toto (Wolff) in his ear trying to say extend for a year and then he's probably got Ferrari saying it's three years or nothing," added the Briton.
"I guess he wants to see through what he started at Ferrari. He went there for a reason, to build something and very much emulate what Michael (Schumacher) had done. Stepping out now, with the progress they have, would be a job half done."
Mercedes have triple world champion Lewis Hamilton under contract for next year while Finland's Valtteri Bottas joined in January with no guarantee beyond 2017.
Vettel, who won his titles with Red Bull, is leading Hamilton in the championship by 20 points after nine of 20 races and Ferrari are keen to renew a contract that expires this year.
Mercedes non-executive chairman Niki Lauda, who played a key role in luring Hamilton to Mercedes from McLaren, dismissed the chances of the German joining when speculation mounted earlier in the year.
Vettel told Horner he was leaving Red Bull for Ferrari in 2014 in a move that stunned the sport.
The German had hoped to emulate Schumacher, the seven-times world champion who dominated with Ferrari in a golden era for the Italian team.
Success has been elusive, however, with Ferrari failing to win a race in 2016 and Vettel making more headlines for angry radio outbursts.
This season he has won three races but was summoned to the governing FIA after driving into Hamilton in Azerbaijan in an incident of road rage behind the safety car.
Horner said his former driver shared some of Schumacher's characteristics in that respect.
"He's got this huge desire within him, the records mean a lot to him," said the Red Bull boss.
"Michael Schumacher was very much his idol and I think what we you see sometimes is that killer instinct of 'I want to win' - sometimes at all costs."
Horner suggested Vettel's recent bad-boy behaviour was also a reflection of his team.
"(Ferrari chairman Sergio) Marchionne has his own style of management. He's a full-on character, he's quite outspoken. The demeanour of the team comes from the top," he said.
"At the end of the day the people that lead the team set the tempo and you can feel Ferrari is a high-pressure place, particularly in this period of time."
(Reporting by Alan Baldwin, editing by Ed Osmond)
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