The Archbishop of Canterbury is working with other Christian churches to agree on a fixed date for Easter.
Justin Welby made the announcement after a meeting of primates from the Anglican Communion in Canterbury.
In the UK, an act of Parliament passed in 1928 allowed for Easter Sunday to be fixed on the first Sunday after the second Saturday in April.
However, this has never been activated and Easter has remained variable, determined by the moon's cycle.
Easter is the most important Christian festival, as it celebrates the resurrection of Jesus Christ following his death by crucifixion on Good Friday.
The archbishop said he was in talks with Pope Francis, Coptic leader Pope Tawadros, and the leader of the Orthodox church Patriarch Bartholomew.
Mr Welby said he hoped the change would happen "in between five and 10 years time".
"I would love to see it before I retired", he said, although he warned the first attempt to make such a change was in the 10th Century.
An Anglican source told the BBC there had been 15 attempts to agree a common date since then.
Easter is on the first Sunday after the first ecclesiastical full moon following the spring equinox, meaning it can be celebrated on a Sunday between 22 March and 25 April.
But the Orthodox church follows the Julian calendar, hence has later Easter celebrations compared with those of Western Christianity.
In 1990, the Vatican approved a proposal for a fixed date, which was subject to agreement with other Christian churches and governments. It has not yet been reached.