Given the furore that has erupted this week in the wake of Sebastian Vettel deliberately flouting team orders before going on to win the Malaysian Grand Prix on Sunday, Webber's future has been drawn into question.
The 36-year-old Australian admitted himself, when emotions were high post-race, that he thought about "many things" over the closing laps as he watched Vettel claim a victory that should rightfully have been his.
Reserve driver Sebastien Buemi has already been mentioned as a likely replacement for Webber should he decide he has had enough.
Horner, though, has every faith Webber will stay this year as he said: "It was the intent of the team that Mark win that race.
"We didn't suddenly give Sebastian instruction and say 'go and pass your team-mate'.
"He (Webber) is big enough to know there was no malice or intent from the team to create any situation like that.
"He is in a car capable of winning grands prix, and hopefully going for a championship, so I've no doubt Mark will see out the season with us."
Horner has confirmed Vettel visited the factory in Milton Keynes this week to offer a fulsome apology for his selfish behaviour.
"He's accepted what he did was wrong, but that he can't turn back the clock," added Horner on Sky Sports News.
"He has apologised to the team, apologised to every single member of staff for his actions because he recognises the team is vitally important, and being part of a team is a crucial aspect of being able to challenge for those championships."
Red Bull advisor Helmut Marko, meanwhile, claims the issue between Vettel and Webber has been "settled".
Marko, right-hand man to team owner Dietrich Mateschitz, said: "They don't have to be completely on the same page, but it must be a solid working partnership.
"Sebastian apologised in the press conference and I think that was the first correct step to make.
"There was a debrief afterwards with the relevant discussions about the race and then there was a handshake between the two drivers. For us now the issue is settled."
Marko has revealed, however, the situation became out of control when Vettel ignored the call to hold station behind Webber after the final round of pit stops.
"We told Sebastian to hold his position because we didn't know what the tyre situation was and both drivers needed to bring home a good finish for the team," added Marko.
"But then came the attack against that strategy and it got out of control.
"You couldn't control it over radio or anything like that. Sebastian the racer came out and took the lead."