Despite the idea being backed by the likes of Ryan Giggs, the governing body has confirmed that there won't be a combined side at the next tournament.
Stuart Pearce led a British team at London 2012 over the summer, the first time since 1972 that a team has been sanctioned, however the formation of the squad was littered with strife.
Both the Scottish Football Association and Irish Football Association refused to release their players due to fears that their status as independent football nations might be threatened.
Ryan Giggs recently joined those calling for a team to be entered in future Games, after captaining Team GB over the summer.
However, Horne has now seemingly confirmed that there will be no representative team in four years' time, but did admit there could potentially be a women's side entered.
"I don't think we will do it again for the men's team," Horne told BBC Radio 5 live. "For the women, we will keep talking to people about it. We are not ruling it out completely, we went through a lot of politics to get here."
Team GB crashed out of London 2012 at the quarterfinal stage, being beaten on penalties by South Korea.