Blizzard has not yet confirmed what will be tradeable or given a definitive answer on how the trading system will work. Previous comments have been made but nothing has been set in stone.
Diablo 4 Trading Systems
Alpha Test Indicators
During the friends and family Alpha test which started in August 2022, a post appeared revealing that there will be restrictions on what items can be traded.
The poster stated that Unique, Set, Legendary, or gold will not be tradeable by players.
This, however, has not been confirmed by Blizzard, and if correct, could change at any point during development.
2021 Blizzard Comments
During the BlizzCon Online Q&A, Blizzard stated that trading between players will be encouraged but they were still figuring out their limitations.
The trading system proposed included direct player-to-player and a clan bank.
2019 Blizzard Comments
In 2019, Joe Shelly outlined their plans adding:
We haven't settled on a trading system yet. We have a philosophy. The idea is the predominant source of items in Diablo 4 should be killing monsters. The same reasoning we removed the auction house in Diablo 3. However, we want to integrate trading more closely in Diablo 4. So, we're exploring several different possible systems.
The one that we are currently leaning towards, one where there would be three types of items.
Items that are tradable all the time, consumables crafting mat, certain items, certain armor perhaps.
There will also be items that can be traded once and then become bound.
And then, some set of items that can never be traded and become bound when equipped. Likely the most powerful items.
In terms of where those three categories we have a lot of flexibility.
It has been confirmed there will be no auction house in Diablo 4.
Previous Diablo Games
In Diablo 2, trading was not limited in any way. Players could trade any item with any other player.
Diablo 3's trading system changed over time. The game launched with the DIablo 3 auction house. The auction house proved to be problematic and was removed from the game on March, 18 2014 just prior to the release of what was dubbed the loot 2.0 update.
Grimiku: Removing the Auction House would fix the problem it created, but that would also create new problems, like chat spam (WTS/WTB [item link]) all day long. That’s definitely not ideal, either. One of the ideas driving Loot 2.0 is that players should not feel that they need to use the Auction House. We don’t mind if players use it, but targeted drops, reduced trash items, better stat ranges, new Legendary effects, and the Mystic should help players feel empowered by the item hunt, and not forced to use the Auction House.
In Diablo 3, any dropped items you see are yours to keep. Preventing others taking it upon the death.
On the launch of Loot 2.0, items such as Legendary and set items became account bound. The Reaper of Souls release also added "Smart Loot" where loot would drop that was more tailored to the class you were playing. This did not effect all loot drops, players would still get items for other classes, just less of them.