Why can't I save my form data into a model db?

When I try to save the info inputted into the form, I get the ValueError:

Cannot assign "<class 'auctions.models.User'>": "Listing.user" must be a "User" instance.

I think that this may be because the model field Listing.user is a foreign key between the Listing model and the User model.

Even when I change Listing.user = User to Listing.user = User() (includes brackets), it returns the ValueError:

save() prohibited to prevent data loss due to unsaved related object 'user'.

So how do I add who the current user is to the model field Listing.user?

models.py:

class User(AbstractUser):
    pass


class Listing(models.Model):
    ...
    user = models.ForeignKey(User, on_delete=models.SET_NULL, null=True)

views.py:

def save_new(request):
    if request.method == 'POST':
        form = NewListing(request.POST)
        if form.is_valid():
            obj = Listing()
            ...
            obj.user = User # this returned the first ValueError
            # obj.user = User() - this returned the second ValueError
            obj.save()
            return HttpResponseRedirect('/')