Horne suffered a bruised hand during Friday night's quarter-final victory over Connacht and was clearly struggling after the incident. The influential No. 9 was unable to use his right hand for several minutes before being replaced by Jack Oliver late in the game.
A key figure in Glasgow's attack, Horne must be considered a doubt for the Murrayfield showdown after missing training on Monday.
Providing an update on the Scotland international, assistant coach Carolan said: "I'd say if George lost his two arms and one of his legs, he'd still want to play at the weekend.
"George is still fighting. He won't train today, he's just a little bit bruised but we're going to give him every chance to get back for Saturday.
"He's doing alright, he's just a little bit tender. At the moment we're preparing and planning that he's available."
Glasgow were hit hard by injuries at scrum-half during their Champions Cup quarter-final defeat to Toulon, when both of their first-choice options were unavailable.
However, Jamie Dobie was close to making his return against Connacht and is now expected to be involved against the Bulls. Carolan is optimistic that both Dobie and Horne could be available, while Ben Afshar is also back in training and could come into contention if required.
"We'd be hopeful that one or both could be available," added Carolan.
"I'll turn it around as well, even for the last 20 minutes, young Jack Oliver in our academy, he stepped up to the plate. I thought he had really good control. Ben Afshar, he's learning. He got injured a few weeks ago but he's back training now as well."