Hi, it looks like the Dell Optiplex 390 has this chipset: https://www.cpu-upgrade.com/mb-Intel_(chipsets)/H61_Express.html

These CPUs should be compatible, though there is no official statement that says so, so try to do some reasearch first. If it's not already, upgrade your BIOS to the latest version.

Optiplex 390 Tech Guide 

A list of compatible CPU's are on pg. 10, or search using "processor."

The top CPU listed is the I5-2400.  If you want to center things around having a Xeon, then you might want to look at refurb Dell Precision's.

Features	Inspiron™ 620/Optiplex 390 VOSTRO 260
Processors	Intel® Core™i3
	Intel® Core™i5
	Intel® Celeron
	Intel® Dual Core
Chipset	H61 - DX11
Memory	1333 MHz DDR3 non- ECC memory only
	(2 x DIMM Slot)
Memory min/max	1GB - 8GB
Video	UMA: 2nd Gen Intel® HD Graphics
	Discrete: AMD Radeon HD 6450
	AMD Radeon HD 6670
	NVIDIA Geforce G420
Operating System	Windows 7 Home Basic 64-bit
	Windows 7 Home Premium 64-bit
	Windows 7 Professional 64-bit
	Ubuntu 18.04 LTS

 

http://downloads.dell.com/published/pages/optiplex-390.html
Intel Core i3-2120 processor (3.30GHz)
Intel Core i5-2320 processor (3.00GHz)
Intel Pentium processor G630 (2.70GHz)

ntel GMA HD 3000 (DT), GMA HD 3000 (NB), GMA HD 2000 (DT), GMA HD 2000 (NB), v.8.15.10.2312, A05 Vista/Win7 64 PV 15.21.11 2312 Gfx/3074 Audio for Sandybridge NB (Huron River)/DT (Sugar Bay) graphics.More details	Windows 7 64-bit Windows Vista 64-bit
Intel GMA HD 3000 (DT), GMA HD 3000 (NB), GMA HD 2000 (DT), GMA HD 2000 (NB), v.8.15.10.2312, A05 Vista/Win7 32 PV 15.21.11 2312 Gfx/3074 Audio for Sandybridge NB (Huron River)/DT (Sugar Bay) graphics.More details	Windows 7 32-bit Windows Vista 32-bit

 

Description	Version	Released
Dell OptiPlex 390 System BIOS This package contains the BIOS update for Dell OptiPlex 390 that runs Windows and DOS operating systems. BIOS is a firmware that is embedded on a small memory chip on the computer's system board. It controls the keyboard, monitor, disk drives and other devices. This package contains update for CPU microcode to address Intel Security Advisory INTEL-SA-00115 (CVE-2018-3639 and CVE-2018-3640). The package also updates to the latest CPU microcode to address CVE-2017-5715.More details	A14	8/7/2018
Dell OptiPlex 390 System BIOS This package provides the BIOS Update on the Dell OptiPlex 390 running the following Operating system: Windows and DOS.More details	A11	10/30/2013
Dell Optiplex 390 System BIOS This package provides the BIOS Update on the Dell OptiPlex 390 running the following Operating system: Windows and DOS.More details	A10	3/20/2013
Optiplex 390 System Bios OptiPlex 390 System BIOSMore details	A09	9/11/2012
DELL,DSK PROG,BIOS,FWH,390,A07,A07 OptiPlex 390 System BIOSMore details		5/31/2012
DELL,DSK PROG,BIOS,FWH,390,,A05 OptiPlex 390 System BIOSMore details		2/15/2012
DELL,DSK PROG,BIOS,FWH,390,A03,A03 -More details	A03	12/14/2011
Dell OptiPlex 390 System BIOS, A02 This package contains the Dell system BIOS update for OptiPlex 390 system. BIOS is a firmware that is embedded on a small memory chip on the computer's system board. It controls the keyboard, monitor, disk drives and other devices. This update includes the latest CPU microcode, Intel Management Engine Firmware and fixes the issue where the hard drive doesn’t get detected.More details	A02	10/25/2011
Dell OptiPlex 390 System BIOS, A01 OptiPlex 390 system BIOSMore details	A01	6/28/2011
Dell OptiPlex 390 System BIOS, A00 OptiPlex 390 system BIOSMore details	A00	5/27/2011