is public to public NAT possible?

[tachyon05]

I have traffic flow like shown below -

A Microsoft public IP > a public IP on our DMZ firewall on prem > NAT > an private IP on prem.

Is it possible to configure FW to forward traffic as shown below?

A Microsoft public IP > a public IP on our DMZ firewall on prem > a Google public IP on internet.

[Flavio Miranda]

@tachyon05 

 Do you mean a NAT from Microsoft to DMZ and then another one from DMZ to Google? 

Dont know which ASA version but   you could use the combination of

nat (outside,inside)

nat (inside,outside)

[MHM Cisco World]

If you use public IP then using IGP with ISP will enough or there is something prevent run IGP with ISP

MHM

[Aref Alsouqi]

What do you mean by a Google public IP on the internet?

[Karsten Iwen]

First, describe what you want to achieve. There may be other/better ways.

[tachyon05]

Thanks everyone.  Here is the current traffic flow at a high level -

Cloud provider 1 public IP 1.1.1.1 >> on prem public IP 8.8.8.8 >> on prem firewall NATs this traffic to a on prem server's internal private IP 10.10.10.10.

We want to move the server to cloud provider 2, and it will have a new private IP 172.16.10.10.  Inbound internet traffic destined to a cloud provider 2 public IP 2.2.2.2 will NAT to this server at 172.16.10.10.

The question is would it be possible for cloud provider 1 to access cloud provider 2 via on prem?  Another words, we want the traffic flow to look like this -

Cloud provider 1 public IP 1.1.1.1 >> on prem public IP 8.8.8.8 >> how to configure >> cloud provider 2 public IP 2.2.2.2 >> NATs to 172.16.10.10.

[Aref Alsouqi]

Are you using FQDNs or IP addresses to access these services? if you are using FQDNs then I think you just need to switch the public IP of the FQDN DNS entry. That will redirect the traffic to the new public IP without having to send any comms for the IP change. If not, I don't believe there is a way to do what you are trying to achieve as I think this more a routing thing than NAT. Also, if you NAT the traffic associated to provider 1 to a public IP of provider 2 it doesn't mean that the traffic will be routed to provider 2. Hence I don't believe what you are trying to achieve is possible.

[foysalisp]

Yes, possible, but it's maybe static IP or Dynamic IP shows you.

Router WAN 1 Public IP and NAT internal Public IP

www.foysalisp.com

My network use this but I am not sure you can try this for test.