Hi all,
I forgot to answer myself as I got an answer from MS.
We can use Intune for that.
We need to create a new app (LOB) and upload the *.msi file we want to use.
Then we must set the "Ignore app version" to No
By the way, as the installation context is User, make sure you assign the app to users or a group of users only.
Once a computer is enrolled, the upgrade time will be minutes. For computers already enrolled, the upgrade can take up to two days.
When a new version of the app is released, we must upload it again to Intune so that it gets deployed on all enrolled computers.
This is one solution. The other one is to install the client only for the connected user (instead of installing for all users) In this scenario, the installation doesn't require admin rights, and so for the updates.
I tested both a couple of days ago and it worked like a charm.
Thank you everyone for your support and solutions (which I may apply in other scenarios. :-)