English FA officials are liaising with the UK Football Policing Unit as they review video footage of the match.
England's 1-0 friendly defeat was marred by supporters who booed the German national anthem and sang songs about World War Two, behaviour which has been widely condemned by leading football figures and British media.
Some noted with dismay how the chants, which included one song about German planes being shot down, had occurred just hours after the terrorist attack in London.
FA chairman Greg Clarke led the condemnation, saying in a statement on Thursday: "The behaviour of a section of the England support in Dortmund ... was inappropriate, disrespectful and disappointing.
Read the full article on eurosport.co.uk: FA pursues 'disrespectful' England fans after Germany game