Williams is joined on the shortlist by Glanmor Griffiths, the former WRU chairman, ex-internationals Tony Gray and Dennis Hughes plus former WRU secretary Denis Gethin.
The election is taking place following the death last year of Keith Rowlands.
WRU chairman David Pickering said: "Keith Rowlands will be a tough act to follow, but the calibre of the nominees ensures that we will have a fine new president.
"All the candidates have excellent attributes and each one of them is well known within Welsh rugby circles.
"If you glance at the list of past presidents you will realise that the clubs of Wales have a proud history of choosing individuals of great ability and integrity to fill this vital role."
Nominations closed last Friday and ballot papers were today being sent out to the union's 241 clubs, four regions and the 21 WRU associate members.
The formal closing date is Tuesday, May 8 and the name of the new president will be announced as soon as the votes are counted and confirmed by the external scrutineers.
The new president will serve until the WRU annual general meeting in October, when there will be another election for a further year in accordance with current article 48 in the WRU constitution.