In short, no.

Roman interactions across the Rhine took one of two main forms, with some variation, for the remainder of the existence of the Empire in the West. These were, diplomatic interactions that were oriented around trying to prevent any one Germanic power from becoming too powerful to handle (and rewarding powers that worked alongside the Romans), and punitive campaigns designed to punish Germanic powers that shook the boat too much, or inflicted some harm on Rome.

The battle of Teutoburg Wald was obviously a massive military defeat for the Romans. Almost the entirety of three roman legions were destroyed with a small handful of survivors who managed to escape. However it was not even the first such disaster in the vicinity of Germania. Several decades earlier, another Roman legion had lost its own legionary standard to Germanic aggression coming from across the Rhine. However the Teutoburg disaster was on another scale entirely, three whole legions were effectively wiped out and their legionary standards were lost, a major religious scandal.

But.... Roman adventurism in Germania did not end with the loss of the three legions under Varus. Augustus, and later Tiberius, oversaw a massive campaign of retaliation aimed against the coalition of Arminius. For the next several years Germania was the site of a series of campaigns designed to break apart Arminius's coalition and avenge the Roman dead, Tacitus even claims in his Annals that the wars were explicitly intended to not be expansionist.

In these campaigns the future emperor Tiberius and his adopted step son, and perhaps later murder victim, and father of the future emperor Caligula, Germanicus, waged a series of wars that were methodical and grinding. Systematically depriving the Germanic opponents of Rome their power bases and resources through scorched earth tactics, and the whole sale slaughter of resisting, and some perhaps not so resisting, tribal groups. Through a series of campaigns and military engagements the German frontier of the Romans was brought into line with imperial wishes. The eagles were recovered, the defeat of Varus avenged, and untold numbers of innocent civilians were slaughtered and enslaved.

The pattern for the next century and a half was to make sure that there were no powerful groups in Germania that wanted to shake off Roman hegemony. Because, while Rome did not invade Germania with the intent of conquering the land, Roman culture and economic domination seeped across the border that legions found too inhospitable. Roman trade goods such as jewelry, metal work, wine, and other luxury goods have been found as far afield in Germania as Scandinavia. Indeed Roman economic power became the new major draw for Germanic groups.

This created a small cascading effect, where within Germania different tribal groups would compete with each other over the access to Roman markets and trade. This kicked off some proto-state formation within Germania itself, and the first evidence of walled cities in Germania date to this time, between the campaigns of Germanicus and the later Marcommanic wars. However this period was not necessarily a time of stability and peace. The internecine wars between Germanic powers (and occasional Roman intervention) eventually led to animosity between the Romans and Germanic powers, even ones that befitted from Roman influence.

The outbreak of the Marcommanic wars is not entirely well understood, and over time different explanations have been given ranging from the implausible, overpopulation, to the more practical, Roman weakness following a bout of plague, and the growing strength of some Germanic powers.

Whatever the cause, the Marcomanni, a tribe from the area of modern day Czechia, and other Germanic powers invaded Roman territory, penetrating the provinces of Pannonia (roughly modern Hungary), and even into Italy itself, and they inflicted a series of disasters on the Romans along the way. Eventually however the empire rallied and Marcus Aurelius counter attacked, after dividing the enemy forces with a series of treaties that broke the Germanic powers apart, and eventually resulted in the defeat of the hostile Germanic powers that had invaded.

In the aftermath of these battles Roman power was reasserted and many tribal groups had to allow favorable terms to Rome that included the establishment of Roman garrisons and perhaps, the establishment of provinces within Germania, specifically in modern day Czechia and Slovenia. This comes the closest to what you ask, and according to the Historia Augusta Marcus Aurelius would have added these as new provinces to the empire had there not been a rebellion in the East. However, this source was written some centuries later than the actual events depicted so it is not certain if there actually were plans to formally annex these territories. These would have been territories beyond the Danube, if not the Rhine, but into lands considered part of Germania.

It is unlikely that these would have survived long however, as the border fell into chaos a few years later that required a new Roman response. Marcus Aurelius died during this campaign. While the campaign was successfully concluded, the new emperor Commodus returned to Rome.

There is a great deal of debate as to whether this period of warfare is the first stirring of the later "Voelkerwanderung" or the period of migrating tribes, that shattered Roman authority in the west, and there are a number of similarities, namely the desire of Germanic powers to settle within Roman territory and gain access to Roman economic power. However it seems unlikely that the Romans seriously considered the establishment of provinces at this time, given both ongoing crises on the border, instability in the east, and the vulnerable position of the potential provinces meant that they never saw actual establishment.