This was reported by the British newspaper "Catholic Herald" on Monday.
The Anglican church of St Dunstan's in Canterbury has announced plans to this effect.
At the same time, in 2035, the 500th anniversary of Morus' execution, the centuries-old relic is to be housed in a shrine and put on public display.
This move could turn the previously tranquil parish in Kent into a centre of attraction for pilgrims, tourists and other interested parties.
According to the plans that have already been submitted to the parish, the Parochial Church Council (PCC) has agreed to initiate the process.
However, the highest church authority must first give the go-ahead. Donations totalling around £50,000 are also required.
Proposals from the parish
According to the information provided, it could take several years for the relic to dry completely.
After preservation, the church plans to either return the remains to the crypt or transfer them to a specially made shrine or stone pillar in the chapel.
According to reports, visitors keep asking when the relic will be made accessible to the public.
The church is therefore calling on the community to collect suggestions as to how Morus' legacy can best be honoured. It also hopes to raise the necessary funds to finance archaeologists and monument conservators.
Thomas More was beheaded in 1535 because he refused to take the oath of royal sovereignty over the church and thus to support King Henry VIII 's break with the Pope.
Thomas More is also known as a spiritual and humanist author; his most famous work is "Utopia", a description of an ideal society.
Thomas More has been the patron saint of rulers and politicians since 2000. His canonisation in 1935 was seen by observers as a signal from the Church against the claims to power of totalitarian states.