Only Munich is standing against Wembley to host the final and semi-finals of the tournament but Germany may pull out to concentrate on bidding for Euro 2024.
Horne, speaking in Monaco, said: "We're really confident with our bid.
"We know what the Germans have been saying. We know that they're thinking about 2024, but nothing has been confirmed."
Asked about England bidding for future tournaments even if Wembley is chosen, Horne said: "I wouldn't rule out looking at Euro 2028."
UEFA is holding Euro 2020 in 13 different countries to mark the 60th anniversary of the tournament and only Wembley and Munich's Allianz Arena have put in bids to host the climax of the competition - the semi-finals and final - ahead of the vote on 19 September.
Horne added: "We are really happy with our bid, it's a really strong bid to host the final and semi-finals. UEFA know us really well - they gave us two Champions League finals in quick succession in 2011 and 2013 so we are really confident we will get a result on September 19. We are in a great position"
Glasgow, Cardiff and Dublin are all bidding for group matches at Euro 2020 and Horne believes at least two of those would be successful.
"I feel confident at least two out of three of Scotland, Wales and the Republic of Ireland will host group games."