Greenacre, a former Phoenix striker, filled a similar role for five games after Ricki Herbert's resignation in 2012.
A statement from the Phoenix on Monday said a "thorough process" was underway to find a new head coach.
Wellington Phoenix chairman Rob Morrison and Merrick will front a media conference on Tuesday at midday in Wellington, with no comment available from the club before then.
Among the candidates for Merrick's job is Rudan, who has just completed a four- year stint at Sydney United culminating in their National Premier League title win.
He is currently assistant coach for Australia's under-20 side.
Auckland City coach Ramon Tribulietx, linked with Brisbane Roar ahead of the 2015/16 season, is also among the candidates.
Tribulietx is in Japan, as Auckland prepare for their Club World Cup playoff against Kashima Antlers on Thursday.
Former Phoenix assistant coach Luciano Trani, who has also spent time at Melbourne City, Brisbane Roar and Adelaide United, and foundation Phoenix captain Ross Aloisi - currently assistant coach at the Roar - are also in the mix.
Merrick said in a statement that he had taken the team as far as he could.
"I take full responsibility for position the team is currently in.
"I feel that I have not performed well enough as head coach, as we have a very strong squad that should be higher up the table."
Merrick, who led Melbourne Victory to A-League titles in 2007 and 2009, took over from Herbert in May 2013, and his initial two-year contract was renewed in March 2015 for another three years.
A Wellington Phoenix statement said Merrick, 63, had been a "consummate professional" during his time at the club. He had been instrumental in overhauling the way the team performed on the field and how it conducted itself off the field.
Merrick had also played a significant role in developing young players through the Phoenix academy, with many now breaking into the first team and representing New Zealand at international level.
"The club understands the decision and thanks Merrick for the hard work and dedication he has put in during the past three years."
2013-14 - Three months after Ricki Herbert resigns, the Phoenix appoint successful former Melbourne Victory mentor Merrick on a two-year deal. The Scotsman can't reverse the results of recent seasons, his team winning seven of 27 games to finish second-last.
2014-15 - Easily the best season of Merrick's reign. With Australian striker Nathan Burns scoring 14 goals, they lead the league a month out from the play- offs. They lose momentum and qualify fourth, bowing out with an elimination final loss to Melbourne City.
2015-16 - The Phoenix lose the services of Burns but still make a decent start. However, injuries and a porous defence sees them drop 10 of their last 13 games to finish second-last.
2016-17 - Despite an encouraging off-season recruitment drive, the Phoenix plunge to six losses from their first eight games - managing just six goals - prompting Merrick's resignation.
