Don't think so, The Tolkien estate owns the rights to that still, its LOTR Amazon has bought the rights to BUT that also means the aphendix of Return of the King that gives you vague details about the 2nd and 3rd ages. I see really three things they could do...
The Second Age - That could involve the buildup to the original wars of the rings that you see the ending of in the flashback opening to Fellowship of the Ring, the forging of the various rings and the story of the Numenoreans who the Gondorians/Aragorn are desended from. You could actually make that into a massive epic if you wanted to perhaps even larger in scale than Jacksons Lord of the Rings films.
The Third Age - Smaller scale than the above but events in Gondor and especially Arnor, the northern kingdom Aragorn was desended from that rules in the area around the Shire and fought the Witch King, again you see a flashback to that in the Hobbit with the Witchking being buried by them. This seems like it would be more Game of Thrones like, more human politics between kingdoms.
Late Third Age - Cover events very close to the point Lord of the Rings starts with perhaps a younger Aragorn played by someone else, that would probably be much smaller in scale and like personal adventures although to me it doesn't really seem like much that's very important bar perhaps the Aragorn/Arwen romance.
