But his comments now indicate that a fundamental change to football's rules could be implemented by the start of next season.
"It's possible we could see [goal-line technology] in the Premier League as early as 2012-13," he said.
"It's easy to make mistakes and we've all seen examples where the referee and assistant referee can't see if a ball has crossed the line or not. We need to support them in decision-making."
Horne's stance was backed by Premier League managers Kenny Dalglish and Owen Coyle.
"I think anything that can help get the proper decision made is going to be very well received," said Liverpool boss Dalglish, who added that the technology might not be needed that often but said it would be "very important" nonetheless.
Lee Sharpe on goal-line technology
Bolton's Coyle said he was fully behind the introduction of goal-line technology.
"We have the best game in world, but the one thing I'd do to improve the game, if I could, is goal-line technology," he said.
"We accept it's a difficult job refereeing and there's human error. But if there's a foolproof system, I'm all for bringing it in.
"Even in my own playing career, I had four or five that were over the line and not given. That would've taken me over 300, rather than being stuck on 297!"
Fifa were previously opposed to the use of technology in football, preferring that decisions remained in the hands of match officials.
That opinion changed following England's game against Germany in the 2010 South Africa World Cup when Frank Lampard's shot on goal was wrongly adjudged not to have crossed the line.
Football's law-making body, the International Football Association Board, is due to assess the results of the current testing phase in March at a meeting in London.
Companies that have matched the strict criteria laid down by Fifa will then be invited to a second phase of testing which will take place between March and June 2012.
IFAB is then due to meet again in July 2012 when a decision on whether to allow goal-line technology will be made using the data from both test phases.
IFAB is composed of the the FA, Irish FA, Welsh FA and Scottish FA - who all receive one vote.
The technology applies solely to the goal-line and only to determine whether a goal has been scored
The system must be accurate
The indication of whether a goal has been scored must be immediate and automatically confirmed within one second
The indication of whether a goal has been scored will only be communicated to the match officials (via the referee's watch, by vibration and visual signal)
Fifa, who act on behalf of the rest of the world, have four votes.
IFAB decisions must be approved by three-quarters of its members, which means Fifa's approval is necessary for any change to the law.
With that deadline of July 2012, Horne did admit it could take too long for everything to be fully tested.
He added: "Whether there is enough time for the technology to be bought, paid for and put into any league or competition for next season, I'm not sure.
"It would be really tight - but it might be possible for next season."
Other sports have already embraced technology with the Winchester-based company Hawk-Eye providing tennis players with the
ability to challenge line calls
They are now seeking to extend their expertise to football and their goal-line system was assessed on Tuesday with all nine competing companies due to be analysed before the end of the year.
The Adidas-backed firm Cairos, whose system utilises an electronic sensor inside the match ball and electromagnetic strips buried under the goal and penalty area lines, are also in contention.
Fifa's testers will travel to League One side Rochdale on Thursday to test "Goalminder", the brainchild of inventors Harry Barnes and David Parden.
Barnes and Parden, both Bolton Wanderers fans, were outraged when a Gerry Taggart goal for their team was disallowed in 1997 and the club went on to be relegated.
Together they patented a system after experimenting with drain pipes and CCTV cameras in Parden's garage.
Fourteen years later, their system - which will retail initially at around £100,000 for a set of two goalposts - uses up to 24 high-definition cameras embedded inside the goalposts.
They claim that the cameras can detect almost instantly if a ball has crossed the line. The information collected by the cameras is then verified by a computer using three-dimensional imaging software located next to the pitch.
If a goal has been scored, an encrypted signal is sent to the referee's wrist watch which triggers a vibration and a visual notice.
Crucially, the entire process takes less than a second, ensuring there is no delay to the game.
There is also the potential to increase commercial revenues through the use of high definition images of goal-line incidents.
The founders hope this spin-off will convince Fifa that there are further benefits to their design.
Incidents such as Frank Lampard's disallowed goal in the 2010 World Cup have added to the impetus for introducing goal-line technology
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