Hamilton's deal is up for renewal at the end of the year and Britain's six-time world champion has already staged preliminary contract talks with the team who have won Formula One's Constructors' Championship for the last six seasons.
Hamilton, who has been linked with a move to Ferrari, is currently paid £40million-a-year. But it has been suggested that his next deal, one which might prove to be his last in the sport, could earn him closer to a staggering £60m per season.
"The logical conclusion would be that Lewis will remain with Mercedes if they can agree terms," said Horner.
"Mercedes will be keen to keep him but it is a question of the financials. The automotive sector is under pressure at the moment and when redundancies are being made, it is difficult to justify record-breaking salaries.
"So, it is what Lewis perceives his value to be. He is an outstanding driver and that comes at a cost or at a value, and I would think that Mercedes recognise that."
Ferrari would be Hamilton's only real alternative to extending his stay at Mercedes, with whom he has won five of his six world titles.
The Italian giants have recently signed Charles Leclerc to a long-term agreement, but Sebastian Vettel's contract expires at the end of the year.
Horner added: "Bernie Ecclestone always said that drivers want to end their careers at Ferrari, but that might be different in Lewis' case.
"He has been unconventional throughout, he seems happy in the environment he is in, and if it is the most competitive environment, why would he want to change that for the sake of driving in a different colour?"
Horner ruled out a move for Hamilton after Red Bull pulled off a major coup by persuading Max Verstappen to sign a new deal which keeps him with the team until 2023.
The young Dutchman won three times last season and finished third in the world championship behind Hamilton and Valtteri Bottas in the sister Mercedes.
"Lewis is the world champion, but Max is the most in-form driver going into the new season," said Horner.
"His wheel-to-wheel race craft is second to none, and the only person I have seen Lewis make mistakes around is Max.
"Max is the coming man. He is 22, on the ascendancy and Lewis is 35. It is inevitable in any sport that there is a new generation coming. We have Max and Charles and it is all set for a really thrilling year."
Red Bull launch their new car on February 12 ahead of the first winter test in Barcelona the following week. The season starts in Melbourne on March 15.