female thread repair: threaded inserts and hole-diameter required
For one of the best known thread repair inserts, Heli-Coils, (I've used them , not associated with them otherwise) an M6x1 insert has a maximum outside diameter of 7.95mm.
Data here.

A better repair in many cases would be to have a welder (person) with a welder (machine) plug the hole, then drill it out and retap it to the size you actually want. Of course, if the original part was under-designed and that lead to thread failure, making it the same as it was won't ensure that it won't fail again the same way. If it's thin aluminum you need to find a good/skilled welder. If the part allows, welding or gluing a nut to it may be a better fix for a too-thin design.