The debate was re-opened this weekend after Frank Lampard's 'goal' was controversially not awarded during England's 4-1 second round defeat to Germany, despite replays showing the ball was clearly over the goal line.
FIFA had previously ruled out the use of systems such as Hawk-Eye, but president Sepp Blatter today stated a new investigation would take place into its use.
And speaking to reporters, Webb stated he was prepared to back any changes if it improved the sport.
"Personally I deplore it when you see evident referee mistakes but it's not the end of a competition or the end of football, this can happen," Webb said.
"We will naturally take on board the discussion on technology and have first opportunity in July at the business meeting."
And Webb, one of the referees at the tournament in South Africa, continued: "I'm open-minded about anything that makes us more credible as match officials...whatever tools I'm given I will use them to the best of my ability.
"It's up to other people to make those decisions. I understand the International Football Association board will look at it again, and we'll see where their deliberations go and whatever decisions are made we'll work to them.
"We will always, I hope, look forward and look at ways at improving the game. I'm a strong believer that football in it's current form is a wonderful spectacle, a really beautiful game. Let's just watch this space with interest and see where it goes."