Fifa president Sepp Blatter is confident the International Football Association Board will recognise the need to implement goal-line technology.
Blatter added his support to calls for video technology after a controversial incident in England's 1-0 win over Ukraine helped eliminate the co-hosts.
Marko Devic's shot crossed the line in the game in Donetsk but was not given.
Goal-line technology could be approved by the International Football Association Board on 5 July.
"I am confident they [the IFAB] will realise that the time has come," Blatter tweeted.
This adds to his tweet of a day earlier, which read: "After last night's match #GLT is no longer an alternative but a necessity."
Uefa president Michel Platini prefers the system of five match officials, but he stated on Monday that he expects the IFAB meeting in Zurich to give one of two goal-line systems currently being tested the go-ahead.
If that is the case, individual associations can decide whether to use the technology in their competitions. That means Uefa could still decide not to implement the system.
The Premier League has previously stated its willingness to make the change.
Uefa's chief refereeing officer Pierluigi Collina has defended the officiating at the tournament, claiming two similar decisions in previous games were correct.
Collina said: "We made a mistake. I wish we hadn't made the mistake but we did. Referees are human beings and human beings make mistakes."