The meeting is understood to be taking place in the Lyric Theatre in south Belfast and is sponsored by Co-operation Ireland, which works to bring divided communities together.
Since it was established in 1979, the charity has created opportunities for groups from the two main religious communities in Northern Ireland and from both sides of the border to learn about each other's traditions and cultures.
The handshake will be viewed as another in a long list of dramatic advances in Anglo-Irish relations.
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