Generalized way of associating custom header "x-transaction-id" in web and desktop based applications

Our company have different rest APIs projects web based as well as desktop based and services. For which we have implemented custom logging mechanism which adds logs for each and every request and information in separate database.

The enhancement requires that we have to attach custom transaction-id header for each request so that we might know which request is going on or which transaction is associated with each of the logs. For this we need generic solution for web and desktop application. In web we can add custom header in request and response but for windows or desktop based services we cannot.

So we might need a generalized way or method so that we don't need to write separate logic for our softwares.

We can create some separate project or nuget package which we refer in each of our application and then it checks which application it is running in. Then add logs or some like this.

Need suggestions.