Former NFL star Jerramy Stevens was arrested for assault early Monday morning following an incident involving his girlfriend Hope Solo ... this according to multiple reports.

Hope was spotted inside a Seattle courtroom this afternoon, where Stevens was facing a 4th degree assault charge stemming from an incident at a home in Kirkland, WA.

According to Chris Daniels at KING-TV, cops say Solo and Stevens were involved in an altercation around 3:45 AM on Monday ... after arguing about where they will live after they get married -- Florida or Washington.

According to Daniels, cops found Solo with a small amount of blood on her elbow ... but she wasn't very cooperative with police.