which domestic company was approached for sponsorship and turned it down?
We can assume with fairly good certainty that these companies were approached:
https://www.ussoccer.com/about/sponsors
@jpeter the maximum sponsorship value will only flow to multinational companies. If the company doesn't have an equal presence in the US, Latin America, Europe and Africa, the value of becoming a "presenting sponsor" is minimized. The companies that have a good presence worldwide will receive the maximum benefit from having their logo on a National jersey. To get a sense of value, take a look at this, which is for the Premiere League: http://www.sportspromedia.com/analysis/premier-league-preview-2018-19-sponsors-kit-deals-every-club