The meetings have been described as routine rather than having any strategic significance, according to a person familiar with the situation.
There is no formal agenda for the meeting between Mr Honohan and Mr Hester, but Ulster Bank’s technology difficulties last year, as well as its strategy for dealing with mortgage arrears, are likely to be discussed.
A spokesperson for the Central Bank declined to comment on the meeting.
Mr Hester will also meet with the top 100 personnel in Ulster Bank to exchange ideas about the future.
It is believed that the RBS chief executive has also scheduled meetings with a number of prominent economists and the head of Sherry Fitzgerald, Mark Fitzgerald, to talk about the economy and the property market.
Ulster Bank has had a difficult number of years in this country.
It was heavily exposed to the Irish property market, which has seen it absorb heavy losses since 2008.
Its parent, RBS, has had to inject over £15bn (€17.5bn) over the past five years to cover losses.
Last year, a technology malfunction caused wide-spread payment problems for Ulster Bank customers. This took a number of months to resolve.
Indeed, during the first few months of last year, there was mounting speculation that RBS was looking to close down or sell its Irish operations.
However, following a company-wide strategic review, it was decided that Ulster Bank would remain a core part of the RBS Group.
RBS is 82% owned by the British government following a bailout in 2009.
Under the stewardship of now disgraced former chief executive, Fred Goodwin, the bank went on a massive acquisition spree from the late 1990s onwards.
However, its takeover of the investment bank, ABN Amro, in Oct 2007 left it dangerously exposed to the US subprime market.
It cost £45bn to be bailed out by the British taxpayer in Oct 2008.
Media reports suggest that the bank’s management is aiming to make a full return to the markets prior to the next general election in Britain, which will take place in 2015.