The interview, conducted on Tuesday by team president Michael Bidwill, was the first in the team's search for a replacement for Ken Whisenhunt, who was fired on Monday after six seasons on the job.
The team has reached out to Andy Reid but had not scheduled an interview. Reid was fired on Monday after 14 seasons as head coach in Philadelphia.
Bidwill plans to fly to Denver over the weekend to interview Denver Broncos offensive coordinator Mike McCoy.
Horton, Reid and McCoy are the only candidates thus far identified by the Cardinals.