The conversation feature in TFS is very basic. If you see it in Asana, it's very user friendly. How can one achieve same, without switching from TFS ?
There are some 3rd Party Plugins from a few different vendors/providers that allow certain non-proprietary features to overlap with TFS and Asana - Zapier for example (https://zapier.com/zapbook/asana/visual-studio-online/) has some "Zaps" that overlay some functionality. It has the ability to custom-create a "Zap" as well, I do not know that much about Asana to reliably tell you that you can overlap both of the features.
Old question, but since Asana is still quite a shallow integration to TFS/Azure DevOps, consider another alternative - https://teamhood.com/use-cases/azure-devops-integration/