Greinke (5-5. 3.97 ERA) is scheduled to start when the Arizona Diamondbacks open a three-game series Monday night at Angel Stadium.
The Angels (38-34) have lost five of their past six to fall eight games back of the final American League wild card.
The Diamondbacks (39-32) dropped their past two after winning six of seven. Their lead in the National League West has dwindled to 1 1/2 games over the Los Angeles Dodgers.
The Angels remain just as starved for playoff success as they were in July 2012 when they acquired Greinke in a deal that sent young infield prospect Jean Segura to the Milwaukee Brewers as part of the package.
It was an exciting time in Anaheim.
Albert Pujols, a three-time NL Most Valuable Player, was in his first season with the Angels at age 32. Los Angeles center fielder Mike Trout was in his first full season in the majors and already an All-Star.
Greinke even did his part, going 6-2 with a 3.53 ERA in the last two months with the Angels, but they missed the playoffs for a third straight season and he opted to sign with the Dodgers in the offseason.
Still in his prime, Greinke went 51-15 in three seasons with the Dodgers and helped them reach the playoffs each year.
Meanwhile, Segura was named an NL All-Star a year after he was traded by the Angels and the 28-year-old shortstop continues to improve. Only now he's in the AL West with the Seattle Mariners and playing a key part.
After Segura was traded to the Diamondbacks and he led the NL in hits in 2016, he was dealt to the Mariners, where he entered the weekend with the second-highest batting average in the majors (.344).
The Mariners lead the Angels by eight games for the final AL wild card.
Meanwhile, the Angels are still seeking their first playoff win since 2009.
They've had success when facing Greinke in the past. He's 3-5 with 3.91 ERA in 12 career appearances against the Angels, including 11 starts.
Several Angels players have also hit well against Greinke during their careers.
They'll try to drop Greinke's season record below .500, something he hasn't experienced this late in a season since 2010.
"As long as I'm able to make good pitches, it's fine," Greinke told reporters after his last start.
The Angels will have one of their most successful starters this season ready to oppose Greinke.
Jaime Barria (5-2, 2.61) has solidified himself as a regular starter for the Angels, both through his performance and injuries to other pitchers.
He took the loss in his last outing, but even that performance included plenty of positives. The 21-year-old right-hander went five innings against the Mariners, allowing three runs (two earned) and eight hits in the 6-3 loss.
"I think Jaime has definitely pitched himself onto our depth chart from spring," Angels manager Mike Scioscia told reporters last week. "We're encouraged at how much he's grown, where he is right now and how much he'll help us this year. There's no doubt, he's pitched his way into more looks for us."
Barria has allowed more than two earned runs in just one of eight starts this season.