Eikon is an end user product. According to the standard Refinitiv contract any data retrieved from Eikon may be utilized only "for the User’s individual use". It may not be distributed or otherwise utilized in any server side or enterprise application, and it may not be redistributed through Web portals or any multi-user Web (or non Web) applications.
If your ASP.NET Core application is targeted at Eikon users, consider Eikon App Studio proposition. If you're looking to utilize Refinitiv data in a Web application targeted at users who may not have Eikon, consider TRKD proposition that comes with a license to redistribute Refinitiv data.
The best way to go about selecting the right Refinitiv product for your use case is to speak to your Refinitiv account manager.
@manjunathreddy, probably, it is possible via REST API. I think that there is no core 2.1 support yet looking at their nuget packages and available platform for them. There is no .net core 2.1 there. Just a regular .net libraries.
I assume that we should wait for someone else to answer us.