Nottingham Forest is living a true dream, normally they would be doing the math to avoid relegation, but it is unbelievable that they are doing the math to go to the European Champions League, we are not talking about the Europa League, but the European Champions League, there are only 4 places and they are occupying one of those 4 places.
https://www.premierleague.com/tablesThey have overcome great teams like Manchester City, Chelsea, Manchester United, Newcastle and are in third place, there are only a few games left for the Premier League to end and they can achieve something big, which would be going to the European Champions League, I doubt very much that this was in the club's management's plans before this season started.
From the image above, only Liverpool and Brighton has the best record in the league in their last five games, having just one draw and 4 wins that's 13 points acquired in their last 5 games. Nottingham Forest on the other hand has done tremendously well for themselves, I totally agree with you when you said, the clubs management didn't plan this before the start of the season. They have already beat their expectations and I think they need just 9 points now to secure a Champions League spot since England too will be having 5 slots for next season Champions League.