Below in right side there is an discrete output signal circuit implementation and as a platform i need to read this signal somehow. I have a discrete input interface. My question is how can use my open/gnd interface to read signal.
The terminologies you are using are not common, so here are my guesses.
The big red box you have outlined is by itself an open/gnd detection circuit. So if that is your "discrete input open/gnd interface", then it is all set to just connect to the ASI connector.
The purple circled part is also an open/gnd detection circuit. It is simpler being not having an isolation relay. That may be more likely to be representative of your "discrete input open/gnd interface". By connecting the purple line to the "B" input, it should work functionally without the added isolation and protection of a relay. But if that does not meet some requirements not specified here, then adding the relay (and diodes) may be the way to meet those requirements.
But these are just guess works to move you forward a little bit. You really need to find out the requirements and what the elements (e.g. discrete input open/gnd interface) really are.