No, since the files listed in the files tab are actually files shared from your OneDrive. You don't want files stored inside of Teams and not OneDrive. So basically what happens when you click attach, if you select OneDrive it will share whichever file you select in place where it's stored with the chat recipients and then add it to the chats file tab.
If you choose attach, it uploads the file to the "Microsoft Teams Files" folder in your OneDrive and then shares with the recipients and adds it to the files list.
If you need further file storage options etc. Then using a Team would be the other alternative solution.
You could also manually Share a Folder with the chat recipients in your OneDrive then post that Link as a tab to your chat or conversation as well.