I seem to recall them wanting refurbished F-16As before the US pacified them with the A-4AR Fightinghawk. I also don't see the US authorizing the F414G for sale to Argentina, probably the most difficult part of the Gripen E to substitute.
I'm not sure how much financial aid the Argentinians receive from the US, and that would certainly be a factor in their decision making, but I'm fairly certain that the Russians would cut them a deal on some MiG-29s if only to annoy the US, and the Chinese are reportedly eager to export the Thunder.
Argentina has options, but it's more interesting to speculate about why they don't pursue them.