Like their opponents, Drogheda suffered defeat in their last outing, and a further setback will leave the visitors at risk of dropping into the bottom half of the standings.
After remaining unbeaten through their opening 11 fixtures of the season, Shamrock will be disappointed not to be sitting in first place.
Nevertheless, with three defeats coming in their last six outings, Stephen Bradley can have no complaints about being edged into second spot on goal difference.
Their only two victories since the middle of May have been against the poorest sides in the division, with their latest defeat coming away at in-form Bohemians.
Shamrock have still only conceded 13 times in 17 matches, the joint-best in the country, but just one clean sheet has been recorded in eight attempts.
Drogheda recorded four successive wins during May, seemingly putting last season's second-tier champions in contention for the top-flight title.
However, three defeats in four, the latest coming against Dundalk, have left Tim Clancy's team nine points off the pace and with more concerns about the teams below them.
While there will be few complaints with a season of consolidation, the door remains ajar for Drogheda to stay in the hunt for their first Premier League crown in 14 years.
Drogheda have gone 209 minutes without finding the back of the net, Chris Lyons scoring their last goal during the 2-1 win over Sligo Rovers on June 12.
Greene could return to the Shamrock side, taking the place of either Burke or Gaffney in the final third.
Ronan Finn is also an option for the home team if Bradley wants to introduce more creativity to his midfield.
Clancy will also make alterations to his Drogheda starting lineup after the narrow reverse at home to Dundalk.
Shamrock Rovers possible starting lineup:
Mannus; Lopes, Grace, Hoare; Gannon, McGann, Mandriou, O'Neill, Scales; Burke, Greene
Drogheda United possible starting lineup:
Odumosu; Brown, Massey, O'Reilly, Kane; Deegan, Heeney; Phillips, Clarke, Doyle; Lyons
We say: Shamrock Rovers 2-1 Drogheda United
With the best defence going up against one of the most productive attacks, there is a feeling that anything could happen in this contest. That said, we cannot ignore Shamrock's position in the table, leading us to predict a narrow home win after a hard-fought battle.