Greece? Surely you jest. Study your history. The socialist Greek government under Papandreou kicked us out of Greece. We closed our bases including on Crete.
A military base in Israel is a non- starter for many reasons.
“Greece? Surely you jest.” (for a US base)
Times change. Maybe they would get hard up enough at some point for a little extra economic activity. Clearly, their left-wing politics (long a priority for agitation by the Soviets, and post-Soviet Russians) has had an Anti-American strain, and their current government is pretty far left.
But under the Post-Soviet “Lily Pad” approach, more smaller bases can be employed vs. fewer larger ones; and local military bases can be expanded for contingency US use, as well as occasional exercises. A low profile deal like that might fly under the political radar, even in Greece, if there were some benefits or security threats that motivated the politicians.
We are already doing a bit of that in Israel, with American Airmen stationed at an Israeli airbase, and given their own facilities to operate.
Even so, the Greece mention is more about their favorable location, than realistic prospects.