Der Spiegel reported it in an article in their 22 May 2010 issue: Historischer Ballast: Ein Geheimdokument belegt: Im Sommer 1990 sondierte ein sowjetischer General, ob Bonn Interesse an Ostpreußen habe. War das ernst gemeint oder eine Falle?, citing a document in the Foreign Ministry archives. The Guardian summarized it in an article in the 31 July 2010 issue.

A message was received in the West German embassy in Moscow from Soviet Maj. Gen. Geli Batenin (I've seen more Web hits as Heli Batenin, or as Gelii). In a later conversation, he indicated that the status of Kaliningrad Oblast was iffy and negotiable. The Guardian summarizes the article as indicating "The Germans, however, were lukewarm about the offer, allegedly telling the Soviets that reunification was the country's priority and that it regarded the Kaliningrad region as a Soviet problem."

(The authenticity of the report or of the offer could be questioned: in 2010, Batenin was dead and Gorbachev firmly denied that any such motion was made.)

To be more precise, the original article says that Joachim von Arnim, head of the political department at the embassy, immediately and on the spot denied any interest, saying that reunification was their only interest (and that it regarded the Kaliningrad region as a Soviet problem). It goes on to explain the real objections, that West Germany thought it was in both the interests of West Germany and the Soviet Union not to give support to Gorbachev's conservative opponents. I think it would have handed them ammunition and I don't mean that metaphorically.

The foremost concern on von Arnim's mind, and anyone who knows about the situation, is that it was poisoned bait. West Germany since Ostpolitik had firmly denied any irrendentism, not just in words but in signed treaties. The four-plus-two process for reunification was starting, and it was delicate at best -- even some of West Germany's NATO allies were inclined against reunification. Had Germany proposed territorial demands outside its borders, violating treaties, and worse, forming another mainland Germany+Prussian pincer on Poland, all looking positively Hitlerian ... not only would the Soviet Union gone into a epic shitfit for the ages, NATO would have joined them, and Poland and Lithuania too. It would have nuked (only figuratively, I hope) German reunification and diplomacy for generations.

Further, while Batenin got some reputation as a reformer, he was also a military advisor to the Soviet Central Committee, and Frank Elbe (a senior Foreign Ministry officer at the time) said that members of the Central Committee had repeately tried to disrupt German reunification.

An even worse objection isn't even mentioned. Most of the German inhabitants fled before the Soviet armies at the end of World War II; the rest were brutally expelled to Germany a few years later. The land had been settled by Russians for generations ... about a million of them. What would Germany do with them? Ethnically cleanse them for German lebensraum?! Even trying to govern them would have been ridiculous.

Also, if another country's claim had been considered, Poland and Lithuania had their own historic claims to the area.

No -- if this was even a real offer, which is questionable now, it was an IED filled with curare-tipped rusty nails.

Follow-up question, for /u/aragonkingofgonder: Where did you hear that Germany was offered Kaliningrad in the 90's?

Another aspect of this issue is the question of why the Soviets would offer to give away the warm water port of Kaliningrad/Baltiysk? None of this makes sense, apart from mischief making.