How to store connection string to session in ASP.NET Core?

I am new to ASP.NET Core and I would like to access the connection string through the session but I am not sure at which point I should set the session value.

I can access connection string in Startup.cs but I think I cannot access HttpContext from there.

Here is the Startup.cs file

public class Startup
    {
        public Startup(IConfiguration configuration)
        {
            Configuration = configuration;
        }

        public IConfiguration Configuration { get; }


        public void ConfigureServices(IServiceCollection services)
        {
            services.AddMvc();
            services.AddDistributedMemoryCache();
            services.AddSession(options =>
            {
                options.IdleTimeout = TimeSpan.FromMinutes(15);
            });

            // Here I can get connection string, but I cannot access Session
            var connection = Configuration.GetConnectionString("devDb2");
            services.AddDbContext<attWebApiContext>(options => options.UseSqlServer(connection));
        }


        public void Configure(IApplicationBuilder app, IHostingEnvironment env)
        {
            if (env.IsDevelopment())
            {
                app.UseDeveloperExceptionPage();
            }

            app.UseSession();
            app.UseMvc();                    
        }
    }