Djere dethroned eighth seed Londero following a 6-7 (5-7) 6-3 7-6 (7-5) victory on the Cordoba clay courts on Friday.
Serbian fourth seed Djere rallied from a set down to earn a semi-final showdown with Schwartzman at the ATP 250 tournament.
World number 14 Schwartzman defeated Spanish fifth seed Albert Ramos-Vinolas 6-0 7-6 (7-0) in one hour, 40 minutes.
Schwartzman, who lost to eventual champion Novak Djokovic in the Australian Open fourth round last month, is eyeing his fourth Tour title and first in his native Argentina.
Cristian Garin – the third seed – and Andrej Martin will meet in the other semi-final.
Garin prevailed 1-6 6-3 6-4 over sixth seed Pablo Cuevas and Martin accounted for Corentin Moutet 6-3 6-2.
Edmund – the eighth seed – defeated Japanese opponent Yasutaka Uchiyama 7-5 6-4 at the ATP Tour 250 tournament on Tuesday.
The Brit won 86 per cent of his first serves as he earned a clash with Dominik Koepfer after one hour, 44 minutes.
German Koepfer defeated last year's runner-up Brayden Schnur 7-5 6-4 in the opening round.
Kevin Anderson – the 2018 champion in New York – was stunned 7-6 (8-6) 6-4 by qualifier Jason Jung, who will face Cameron Norrie after the seventh seed beat Brian Shi 7-5 6-3.
Elsewhere, Jordan Thompson accounted for veteran Ivo Karlovic 6-3 7-6 (7-2), Yoshihito Nishioka outlasted Henri Laaksonen 6-3 0-6 6-2, Paolo Lorenzi prevailed 4-6 6-4 6-0 over Danilo Petrovic and Go Soeda went down 6-2 6-7 (2-7) 6-3 to Kwon Soon-woo.
At the Argentina Open, Cecchinato's title defence was ended by Roberto Carballes Baena in the first round.
Cecchinato was upstaged 6-4 7-6 (7-3) by Carballes Baena, who saved five of six break points on the clay in Buenos Aires.
Next up is Casper Ruud after the eighth seed blitzed Pablo Andujar 6-2 6-3.
Fellow seed Laslo Djere and Albert Ramos-Vinolas also progressed to the last 16, along with Facundo Bagnis, Juan Ignacio Londero, Pedro Sousa, Pedro Martinez and Jozef Kovalik.
Londero progressed to the last eight of the ATP 250 tournament thanks to a 6-3 6-3 win over Argentinian compatriot Pedro Cachin on Thursday.
Cordoba was the scene of Londero's breakthrough ATP Tour title last year, the Argentine player capping a fairytale week by overcoming countryman Guido Pella in three sets.
Next up for Londero on the red clay is Serbian fourth seed Laslo Djere, who beat Spanish qualifier Pedro Martinez 6-3 6-4.
"I was a little nervous and that's why I talked to myself a lot and that's how I got in the game. The way I have to activate [myself] is by encouraging myself a lot. If I keep quiet, that doesn't happen. It was a game with many nerves for me, and I am glad I won it in straight sets," Londero said.
"For me, it is more a motivation than a pressure to play in Cordoba and try to defend the title. If I had to defend the tournament elsewhere, without having the support of my family, my friends who can see me live, the truth is that I think it would be more difficult anywhere else. I have been having a good time."
Albert Ramos-Vinolas – the fifth seed – outlasted Pablo Andujar 6-3 6-7 (4-7) 6-4 to set up a clash with Schwartzman, who defeated Jaume Munar 6-1 7-5.
Cordoba was the scene of Londero's breakthrough ATP Tour title last year, the Argentinian capping a fairytale week by overcoming countryman Guido Pella in three sets.
Back on the red clay following a first-round loss at the Australian Open in January, eighth seed Londero defeated Italy's Marco Cecchinato 6-2 7-5.
Londero – playing the night session – did not face a break point and won 70 per cent of his first serves, much to the delight of the home crowd at the ATP 250 tournament.
Next up for Londero is fellow Argentine player Pedro Cachin, who crushed Hugo Dellien 6-1 6-1 in just 58 minutes.
Spanish fifth seed Ramos-Vinolas beat local qualifier Facundo Bagnis 6-4 7-6 (7-3), despite wasting a match point at 6-5 in the second set.
It will be an all-Spanish affair in the last 16 after Pablo Andujar accounted for Filip Horansky 6-2 6-2.
Elsewhere, Jaume Munar (6-4 6-3 against Leonardo Mayer), Andrej Martin (7-6 [7-5] 6-4 over Federico Coria), Pedro Martinez (4-6 6-3 6-4 against Federico Gaio) and Corentin Moutet (6-4 6-3 over Thiago Monteiro) also progressed to the next round.
Thompson overcame big-serving American Isner – who had a first-round bye – 7-6 (7-2) 6-7 (3-7) 6-3 in New York on Thursday.
Isner was playing his first match since being forced to retire from his third-round clash against Stan Wawrinka at the Australian Open due to a foot injury.
Thompson lost to Isner in last year's New York quarter-finals but the Australian turned the tables after two hours, 31 minutes.
"I'm pretty stoked about that. That was a tough match," Thompson said. "I didn't get too many looks at Isner's serve, but managed to get the one break and held onto it."
Standing in the way of Thompson and the semi-finals is Andreas Seppi.
Opelka opened his title defence by cruising past Yoshihito Nishioka 6-4 6-4 at the ATP 250 tournament.
Next up is qualifier Jason Jung, who stunned seventh seed Cameron Norrie 6-4 6-4, Kyle Edmund – the eighth seed – was too good for German Dominik Koepfer 6-2 6-4.
At the Argentina Open in Buenos Aires, Diego Schwartzman and Guido Pella moved through to the quarters on clay.
Schwartzman – the top seed – prevailed 6-3 4-6 6-2 over Federico Delbonis and second seed Guido Pella survived a marathon against Facundo Bagnis 7-6 (7-2) 6-7 (2-7) 6-4.
Fellow seeds Laslo Djere and Albert Ramos-Vinolas, however, crashed out following defeats to Juan Ignacio Londero and Pablo Cuevas.
