Regarding Giggs, after retiring from the Wales national team, he did talk about his desire to coach again soon. It should be considered, but I think the chances are also small.
Giggs should not be considered.
Manchester United need a very experienced coach that can handle a team if they're to sack Ten Hag. There's no point getting an inexperienced manager to replace Ten Hag. Also, I think the performances of all the former Manchester United players as coaches should let anybody know that having a former United player as coach is a disaster.
Manchester United had the opportunity to look for another Manager, but they decided to stile with Ten Hag, now they have to stick with him till the end of the season because it will be a wrong decision to sack him and hire another mediocre manager.
Expecting Simone Inzaghi to leave Inter Milan mid season where he's doing well to go coach Manchester United is laughable because it's not going to happen.
I've been singing it since that Manchester United won't get better with Ten Hag, no matter how long they give him and no matter the players they sign for him. A good manager should be able to make this Manchester United team a competitive team.