Your system CPU is well before the generation 8 CPU minimum requirement for Windows 11. You should be able to run Windows 10 but are not going to be able to run Windows 11 being well below the minimum system requirements. Run the PC Health Check app found here for more information.

to add to what Jocean wrote, you do not need the tpm at all to use windows 10 ( it would be needed only to activate encryption, and anyway there's a way around it to do it without a tpm too ), and is possible that free win7>win10 upgrades are still allowed

@MakesOwnWeather , Re:  Does anyone know of a way to add this to a T7500 so I can run Win 10 or Win 11?

You don't need to add TPM module to your system to install Windows 10 or 11.

For Windows 10, just use Windows creation tool to create a Windows 10 installation USB drive to perform a clean install.  Make sure to back up all your data as the process will delete all partitions.  During installation, click the box don't have key and select Windows 10 pro to install.  Once complete, you can connect online and use your Win 7 Ultimate product key to activate to Win 10 pro.

To install Windows 11, you will need to search online, many website give instruction for the method to create an installation drive and the detail is not allowed to post here.  But in general, the installation process will be simple as for Windows 10, it won't check for TPM or any other requirements.

Use a spare drive for testing so you can always put back your old one if you don't like the new Windows.

@MakesOwnWeather   please press the blue Accept as Solution button below if this post answers your question. 

The following apps will no longer be installed on new devices or when clean-installing Windows 11. They are available for download from the Store:

• 3D Viewer
• OneNote for Windows 10
• Paint 3D
• Skype

T7500 is legacy bios and therefore does NOT HAVE Secure boot so there is no option to install windows 11.

TPM 1.2 is required for the Mosetup solution.

So if you have a Dell Precision T1700 with TPM it works fine.

Ways to install Windows 11
Install Windows 11 with TPM 1.2 and unsupported CPU using Mosetup

Windows Registry Editor Version 5.00

[HKEY_LOCAL_MACHINE\SYSTEM\Setup\MoSetup]
"AllowUpgradesWithUnsupportedTPMOrCPU"=dword:00000001

Warning:

Microsoft recommends against installing Windows 11 on a device that does not meet the
Windows 11 minimum system requirements. If you choose to install Windows 11 on a device
that does not meet these requirements, and you acknowledge and understand the risks,
you can create the following registry key values and bypass the check for TPM 2.0
(at least TPM 1.2 is required) and the CPU family and model.

Registry Key: HKEY_LOCAL_MACHINE\SYSTEM\Setup\MoSetup

Name: AllowUpgradesWithUnsupportedTPMOrCPU

Type: REG_DWORD

Value: 1

Note: Serious problems might occur if you modify the registry incorrectly
by using Registry Editor or by using another method. These problems might
require that you reinstall the operating system. Microsoft cannot guarantee
that these problems can be solved. Modify the registry at your own risk.

Thanks, Man of Gold, for your reply.  Do you have a suggestion re which is best, 10 or 11?

BTW, one of my three T7500 machines has lost its genuine key.  Do youhave any suggestion on how to restore it?

Thanks speedstep for your input.  It is a lot to digest, but I will go through it all.  

You mentioned I should be ok with a T1700.  Is this a typo?

BTW Do you have a suggestion re which is best, 10 or 11?

BTW, one of my three T7500 machines has lost its genuine key.  Do youhave any suggestion on how to restore it?

Thanks in advance!

Hi and thanks for your input, JOcean.  I do have dual x5690 CPU which mean I have 12 cores.

So Win 10 does not have TPM requirement or do I have TPM but do not realize it?

BTW, one of my three T7500 machines has lost its genuine key.  Do youhave any suggestion on how to restore it?

@MakesOwnWeather 

There is no restoring a COA key.  If windows 10 was activated it will stay activated as long as the machine is online every 180 days.

10 is fine and its good till 2025.

I'm using 11 on a precision T1700 so that I know what the differences are as well as the requirements.

Legacy SLP keys in bios only work for Dell OEM media for xp, vista, 7

Windows 7 SLP Keys 

@MakesOwnWeather , Windows 11 looks better, Windows 10 more user friendly and features from older Windows.  But it is more of personal preference, not everyone feel the same.

If one of your machine lost its key, you would want to upgrade it to Windows 10 first to receive a digital license, after that, you can reinstall Windows 11.

Each computer user has different knowledge, I don't want to insult you with basic instruction but also do not want to overwhelm you with information that sound foreign to you.  When you are running into issue, just throw the question in here, I am sure someone will have the answer

Hi, I think I may be able to help. This link if allowed shows a step by step guide. Read the entire step by step guide before doing it because you don`t want to miss a step, also I would suggest having a pen and paper handy.  https://kodyaz.com/articles/how-to-activate-windows-7-by-phone.aspx