World football's governing body sees the technology, which is in competition with Danish-based GoalRef, in use at St Mary's and it could be in place as early as next season
The technology uses multiple camera angles which in turn sends a signal direct to the referee in under a second telling him whether the ball crossed the line or not.
Hawk-Eye's managing director, Steve Carter is hopeful that his company's product will be the one chosen if Fifa decide to introduce the technology to football matches.
He told Sky Sports: "Every stadium is different. Anything from three weeks to a couple of months. It's all stadium specific.
"We aren't thinking that far ahead at the moment. Anything is possible.
"I suppose a good sporting analogy would be that we are in the semi-finals of the competition at the moment and we just want to concentrate on winning our semi."Hawk-Eye is on competition with Danish based GoalRef, with a preferred product to be revealed by Fifa on July 2.
The Football Association's head of senior referee development, Neale Barry, insists that the technology could be implemented as early as next season.
He said: "If it's licenced there is no reason - assuming the Football Association decide to implement it - that they can't install it in time for the next domestic season."
Hawk-Eye will be available in the Hampshire FA senior final, where they are based, for research purposes only but Carter wants things to be ran at his own pace.
He added: "If I felt things were being rushed for a specific league, I would be actually urging people to slow down and make sure the technology is right."