Hamilton is on target to match Michael Schumacher's record of seven world titles if he continues on his current trajectory this season and is also likely to beat Schumacher's all-time career win record of 91 victories.
Such is Mercedes' advantage over the rest of the field this season that Hamilton has won five of the seven events so far, with Bottas taking one victory in Austria and Red Bull's Max Verstappen scoring a win in Great Britain.
Bottas started the season looking like Hamilton's biggest rival, but Verstappen has emerged as his closest competitor in the drivers' championship so far.
Mercedes has always taken pride in giving its drivers equal opportunity in their battle for the title, but Horner believes Hamilton has been given preferential treatment this year.
"It's obvious that Mercedes favours Lewis," Horner said. "You see it on strategy, the positioning of the cars and so on.
"Why wouldn't they have put Bottas on a two-stop, for example, in Spa [at the Belgian Grand Prix last weekend]? That would have given him the opportunity to win the race.
"The problem is that everything is geared towards Lewis this year on his record-equaling campaign. The reality for Valtteri is that unless he qualifies ahead, he hasn't got a chance."
Asked about Verstappen's chances of taking the fight to Hamilton now that he is 47 points behind the Mercedes driver with 10 races remaining, Horner said it was clear from the start of the season that Red Bull was the underdog.
"We are still very much the outsiders," he added. "Hamilton and Mercedes have been the favourites for both titles, as they were coming into this season, but there is still a long way to go as we aren't even at the halfway point yet.
"We never give up and we treat every race like a cup final and we are in a position whereby we have nothing to lose."