This sounds like a foreign grantor trust that owns PFICs. Whether or not US tax is due is moot - it arguably adds Forms 3520A, 3520, FBAR, 8621 (or whatever the HIRE Act version will be), 8938 plus possibly an 8833.
There may be zero US tax; contributing could reduce tax in some circumstances...but it will add dozens of additional pages to your US returns for the rest of your days. This is not an easy choice.