The BBC reports that Bishop Harper in an interview with the Irish Times says that the ban on Catholics becoming the British monarch should be abolished.
The Act of Settlement of 1701 bans Catholics, or those married to Catholics, from ascending the British throne.
Bishop Harper, who was born in Tamworth in Staffordshire, is to succeed Dr Robin Eames who retired in December.
The new primate-elect said the Act "belongs to its time and we should move on", but that its repeal could have implications for the Church of England.
As well as being the head of state, the British monarch is governor of the Church of England.
Bishop Harper told the Irish Times that the disestablishment of the Church of England - separating church and state - was something it would "not only get over, but would be the better for it".
Previously, Westminster Cardinal Cormac Murphy-O'Connor has said under the terms of the Act, Prince William "can marry by law a Hindu, a Buddhist, anyone, but not a Roman Catholic" and still be king.
The relevant part of the Act states: "That all and every person and persons, who shall or may take or inherit the said Crown, by virtue of the limitation of this present act, and is, are or shall be reconciled to, or shall hold communion with, the See or Church of Rome, or shall profess the popish religion, or shall marry a papist, shall be subject to such incapacities."
Catholic monarch ban 'should end' (BBC News, 18/1/07)
Royal Family member to wed at Vatican (CathNews, 1/11/07)
Catholic congratulations for Queen on 80th birthday (CathNews, 26/4/06)
British Cardinal makes history preaching to Queen (CathNews, 14/1/02)
Call for Queen to lose title as head of Church (CathNews, 16/6/03)
19 Jan 2007