Was there ever a Japanese plan to do this? It seems like a much easier way not only to put enormous pressure on the Soviets (fighting a two-front war), but also to gain and hold resource-rich territory than attacking the U.S. Pacific Fleet three years later.
Japan and the USSR were in conflict even before the outbreak of the war in Europe. As early as 1932 there were border clashes between Manchukuo/Manchuria and Mongolia. Over the course of the next 7 years there would be hundreds more clashes, some of which resulted in fairly significant casualties. Eventually in 1939 this culminated in the the Battles of Khalkin Gol in which the Soviet Union was able to more effectively mobilize larger amounts of troops and particularly tanks. Despite heavy casualties on both sides the USSR proved victorious. Following this a cease-fire was signed and though the two nations were effectively enemies they established a status quo of peace.
As to why Japan didn't go back on this truce when Operation Barbarossa was launched, there are tons of factors. One is that the soviet center of industry was being shifted to the Ural Mountains which are still quite a distance from Mongolia. If Japan had launched an invasion it would mean trekking through the worst of Siberia to get to the fortified Ural region and then waging a war in some of the most hostile conditions imaginable. The trope of "not invading Russia in the winter" is certainly way overblown, but it would not have been an easy campaign invading the USSR from the east. Furthermore the early successes of Barbarossa reassured Germany that it would be an easy campaign, and outside help seemed unneeded until the reality of the Soviet resistance began to sink in. Additionally Japan was entrenched deeply in its war with China and its various armies. While invading the USSR would've benefitted Germany, there were far more lucrative and easier to seize places for Japan to turn its attention to, specifically the colonies of the pacific and south East Asia. By the 1940s Japan was resource starved and the American led embargoes were taking a heavy toll. As such their immediate needs lay in claiming resource rich areas to fuel the heavy costs of a war in China that had lasted a decade. The attack on America was probably ill-advised in retrospect but it was a direct response to the resource starvation that Japan was feeling as a result of America. The USSR, despite being an ideological enemy, was not concerning itself too much with Japanese affairs and seemed content to allow Japan to wage wars south of its borders. At the time of Barbarossa it seemed that Germany would be able to deal effectively with the USSR while Japan would get to focus its attention elsewhere.