Short answer: no, not really, and it wasn't an option anyway.

Long answer:

After WW1, there was substantial public opinion that favoured unification with Germany, even the Socialist leaders such as Karl Renner spoke out in favour and the new republic was actually called „Deutschösterreich“ (German Austria), and was declared to be a part of Germany. An entire political movement („Großdeutsche“, greater Germans) formed and the whole thing culminated in the so-called „Anschluss“ in 1938, which many Austrians greeted enthusiastically while many others didn’t oppose it either (although that, of course, has many other reasons).

Then the war happened, and already during it, there were movements to make sure Austria would get better treatment than Germany once it was defeated. In the Moscow Declaration of 1943, the allies decided that while they would fight to make Germany surrender unconditionally (which then happened), the situation regarding Austria would be a liberation. The declaration specified two points in particular:

a) Austria was the first victim of Hitler’s/Germany’s aggression and should be liberated

b) However, Austria had also played a role in the crimes of the Nazis and could not escape responsibility for the part it had played

Conveniently for Austria after the war, the first of these two points was very much put in the spotlight, leading to the creation of the „Opfermythos“ (victim myth) that essentially remained mainstream opinion until the 1980's (see in particular the election of Kurt Waldheim as president and his Nazi past). The country saw itself as Hitler’s first victim and did all it could to distance itself from Germany.

Two more aspects made sure another „Anschluss“ to Germany was near impossible:

a) Austria gained its indepence in April 1945, with a provisional government set up under Karl Renner. While the country remained under allies occupation until 1955, the first free elections were already held in November 1945 and Austria got a pretty good start towards regaining its souvereignty – while in Germany, the situation was much more difficult and this would have made reunification rather complicated.

b) It was very much in the interest of the allies (especially the Soviet Union and France) to oppose a possible „Anschluss“. Especially Stalin wanted post-war Germany to be as small, splintered and weak as possible to never again allow it to attack Russia. France had similar views. Stalin and others would have completely opposed movements to re-unify Austria with Germany.

So, to summarise: Austria after 1945 wanted to escape blame for Nazi crimes and thus distanced itself from Germany and possible reunification. The movement of a greater Germany including Austria lived/lives on in far-right Austrian politics including, most notably, the FPÖ, which is now in government.

Also note that it admittedly did take a while for Austrians to adapt their identity, and many did continue to see themselves as German rather than Austrian well into the later 20th century.

Sorry for spelling/formatting mistakes, typed this on my phone and can provide clarification and sources later.