The minor premiership is up for grabs while fourth-placed Eagles are the form side heading into the final three rounds of the Illawarra mens Premier League squash competition.
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Greyhounds lead the five-team top men's comp by 12 points - less than one victory - but have lost two of their past three games.
But the Eagles are arguably the team with momentum after three straight wins.
The Premier League was restructured this season with players assigned to teams rather than playing for their normal side to even the competition after Eagles won five of the past seven titles.
"The evening up of the comp has certainly worked," Eagles veteran Troy Mountford said.
"Everyone feels they are a chance of winning week to week and it's going to be a great battle for the title.
"Eagles are on a bit of a run but Greyhounds, Raptors and Bulls (third) will fancy they can make the grand final."
Greyhounds will pick up no points for the final round bye and need to beat Bulls on Wednesday at Dapto Squash Centre (7pm) in round 13, plus beat Eagles the following week to clinch the minor premiership.
Greyhounds beat Raptors 17-11 in round 12 to get their season back on track.
Raptors have the round 14 bye and after two straight losses face last-placed Superoos in a vital match on Wednesday night (7pm) also at Dapto Squash Centre.
Third-placed Bulls know a win in round 13 against Greyhounds would really set up their season, while Eagles have the bye this round and face Greyhounds and Superoos before the finals.
Superoos have to win their final three games against Raptors, Bulls and Eagles to make the top-four semi-finals which start on May 27.
Ladder: Greyhounds (164), Raptors (152), Bulls (138), Eagles (119), Superoos (99).