Hawk-Eye managing director Steve Carter believes their goal-line technology is on course to be licensed by FIFA, but would not speculate on its use in the Premier League next season.
The British company and German-Danish firm GoalRef are vying to be approved as authorised suppliers of goal-line technology and were chosen for the next testing phase by the International Football Association Board (IFAB).
The second phase of testing on Hawk-Eye's system began on Thursday at the St Mary's Stadium in Southampton, where independent body Swiss Federal Laboratories for Materials Testing and Research (EMPA) undertook on-field research.
The process will continue on Friday and next week the system will be tried in the Hampshire Senior Cup final between Eastleigh and AFC Totton, with another match to be tested as well before the IFAB decide on July 2 whether to approve the system.
"It is tremendously exciting and it will be the highest profile and biggest sport that we do if we're successful," Carter said. "FIFA have appointed an independent scientific research institution called EMPA and they basically set a series of tests that we need to perform against.
"Subject to Hawk-Eye passing those tests, hopefully we will be approved for use as an official goal-line technology adjudicator. All of the results are confidential. We don't get to find out, but every indication is that everything is running very smoothly.''
Hawk-Eye's system uses seven high-speed cameras at each end of the ground to calculate a three-dimensional position of the ball, while GoalRef uses a chip in the ball which is monitored by magnetic fields in the goal.
Both could be available for the start of next season if approved by the IFAB, but Carter was keen not to talk about timescales.
"It varies from ground to ground on how long it takes to install the system," he said. "At the moment all of our concentration and energy is on doing as well as we can, making the technology as good as possible and making sure that we get excellent results from phase two.
"The roll out of that technology is something we have a lot of experience in through our work with cricket and tennis, but it is not something we are focusing on at the moment."
Asked if it was feasible to have it in place for the start of the 2012-13 season, he added: "It is impossible for me to say right now. You would have to survey the grounds and there would be a lot of logistical things that we would need to go through and at the moment I don't have that information."