Mussolini wanted Greece as a satellite/client state but not necessarily occupy it's territory.

There are four major aspects to this:

The Adriatic sea:

it was considered if not italian territory, at least inside it's inner sphere of complete dominance. Influence over Albania, which would later evolve into annexation, played a major role in this strategy. Greece had territorial ambitions against Albania, (souther parts of Albania hosted a big Greek minority), so they went head to head against one another since 1912.

This is obvious in 1923's Corfu Incident where an italian general, part of a committee sent to arbitrate over border demarcation between Greece and Albania was murdered inside Greek territory. Italy bombed the island of Corfu and disembarked thousands of italian soldiers effectively occupying it. Mussolini's rhetoric, among others, reminded again and again that Corfu had been Venetian for centuries casting doubts over the legitimacy of greek sovereignty. Greece was forced, amidst League of Nation's complete inability to intervene, to succumb to italian demands.

The Cham Issue

As southern Albania hosted a big Greek minority, the Epirus region of Greece hosted a Cham minority. This albanian muslim community had escaped the exchange of populations between Greece and Turkey and parts of it had emigrated in Albania after systematic Greek state pressure. Their demands were fomented by the Italians as a tool of questioning the terrorial integrity of Greece and to act as counter-balance to Greek claims over its minority in Albania.

The question of the Dodecanese Islands

The Dodecanese Islands were occupied by Italy after the italo-turkish war of 1912 and were for all intents and purposes inhabited by Greeks. The Italians in 1919 and 1920 had agreed to cede the to Greece in exchange for Greek recognition of italian "influence" in south Anatolia but this agreement fell through with the victory of nationalistic turkish forces under Mustafa Kemal, (aka Ataturk).

Given that Italians had little to show for their participation in WW1, these islands assumed a political significance greater their strategic one and Mussolini was adamant about keeping them while Greece formally demanded their incorporation to Greece. While Greece could do little to enforce its claims, they remained another area of contention.

The alliance between Greece and Great Britain

Greece had maintained an alliance with Great Britain which directly challenged Italian authority over the eastern Mediterranean. Quite interestingly this alliance became even stronger when a fascist dictatorship was installed in Greece under Metaxas, which for some aspects copied the italian fascist model. This alliance, together with other system of alliances like the one with Jugoslavia, made Greece less susceptible to italian demands although Greece was highly aware of the disparity of power between these two countries.

This tactic is obvious of how Greece treated the sinking of the cruiser Elli, while still neutral. An italian submarine acting on verbal instructions, which still are non-verified but can be attributed to Mussolini, torpedoed the old cruiser which anchored in the island of Tinos to pay homage to a religious holiday. Greece immediately verified the nationality of the submarine but refused to publicly acknowledge it in fear of a direct military engagement while at the same time preparing for an italian invasion.

So to recap: Italy directly occupied greek islands in the Aegean and fomented Cham claims over Greece. Greek strategic interests lay exactly in the path of italian expansionism, while at the same time being the weakest neighbor of an aggressive fascist italian state. Mussolini demanded Greece becoming a client state and when international instances allowed it, he attacked militarily Greece in the 20's and again before WW2. So Greece had more than suspicions over italian expansionism and were quite prepared, at least as far as a small nation could, when Italy attacked in October 1940. This resulted in italian defeat and greek occupation of southern Albania, at least until the Germans came to the rescue.