Go into macOS Recovery (turn on your iMac and immediately press and hold the Command (⌘) key and the letter R on your keyboard until the Apple logo or spinning globe appears on your screen, then let go of the keys). Wait for the macOS Utilities window to appear on your screen, then choose Disk Utility, then press Continue and run First Aid on the Startup Volume, which is most likely your Macintosh HD. After First Aid repairs it or says that it's successfully completed the check on your Macintosh HD (with a white checkmark and an OK on a green background), shut down your iMac. Boot up your iMac normally, plug in your External HD for Time Machine backups to your iMac, and now you should be able to immediately begin backups on Time Machine. Please note: The preparing backup sequence on Time Machine will initially take awhile (like maybe 45 minutes or more) before Time Machine begins backing up.
Be aware that you can get quite a number of backups done on multiple backup disks for several days, before you may have to do it again (the procedure isn't too time-consuming anyway), but at least it's a quick fix to that devilish red circle with the "little white i" inside of it on the Time Machine window.