Open up the appliance via port 5480 (i.e https://vcsa.company.local:5480)
Log in with the root account, and under Networking click the Manage tab. DNS settings are located here. Ensure it is set correctly.
I logged into vCenter Manager appliance and checked that DNS is correct.
It contains correct internal DNS entry which points to internal DNS server and correct internal host name, which properly resolves.
I also checked on internal DNS server to make sure that A record exists for the vCenter host. It does.
For some reason when I use update feature inside the vCenter appliance center I get good response inline vSphere web client.
BTW, can I go ahead and use update option from here?
The problem would not lie on the appliance but on the ESXi host. That message means the host was unable to stage patches from VUM, which, as you know, is not built-in to the vCSA 6.5. Can the ESXi host(s) resolve the name of the vCenter Server? Can they do so with forward and reverse DNS queries? If the answer to these questions is "yes" then you'll need to look at /var/log/esxupdate.log after producing this message and scanning to the end to see the exact reason.
The updates in the picture above will update the appliance which you can definitely go ahead with.
Are all hosts failing to update? Have you gone through and tried to update each host individually to see if you get the same result?
How is it possible that in the image above I have version 1f available but in my account I can only see 1e?
Also what do you exacly mean by saying check DNS on ESXi host?
Lets suppose that for simplicity I only have one ESXI host on which the vCenter appliance is running.
Looks live VMware is confusing us!
vCenter 6.5.0f (Released 14th of Nov 2017)
vCenter 6.5.0U1e (Released 9th of Jan 2018)
You will be updating you vCenter to the Update 1 release of 6.5.
As daphnissov alluded to in his comment, check DNS on the ESXi host and ensure it can resolve the vCenter appliance. Even though the the appliance is running on the host, the host will need DNS to find vCenter.
You can check this either via the console or the web interface. Below is a screenshot of the web interface of one of my hosts:
Use putty to SSH to your ESXi host and do a ping test to vCenter (using the host name) and see how you go. If that fails try to ping the vCenter with the IP address and see if you get a reply. If that fails also, you probably have something else going on in your network. If it succeeds then its more than likely a DNS issue.
Hope this helps