The 3670 uses the Intel B360 chipset, and that supports 8th and 9th Gen i3, i5, i7 and i9 processors.  However, this particular Dell model's Setup and Specs document - which is easy to look up under Dell's Support links - says that the 9th Gen i3, i5 and i7 is supported.  The i9 is not listed, however. It also supports the Pentium Gold and Celeron G series.  But, I assume you aren't looking that either of those. Here's the link... [URL] It's on page 12. As to the max CPU size?  Whatever is the highest each line goes to.  Probably the i7-9700T.  Now, the 8th Gen i7-8086K has a higher base and turbo speed rating, but also pulls more power, and probably a little less efficient. So that's the trade-off you'll have to consider. 
Currently I have an 3670 with a 8th Generation Intel(R) Core(T M) i5+8400 processor (9MB Cache, up to 4.0 GHz), 32GB of DDR4 2666Mhz ram, MSI, GTX 760 Video card, 650w PSU. That is all the important parts. The CPU is removable. I cannot seem to find out what the max size CPU will fit on the motherboard? I have the latest BIOS update. Everywhere I look, No one seems to know.
Inspiron 3670 CPU max size allowed.