No.
In the case Manchester United wins the Europa league this season, they will qualify for the champions league and the 5th placed team of the premier league will qualify for the champions league too.
It's even possible that 7 english teams will take part in the champions league next season. That will happen if Aston Villa wins the champions league this season without ending the premier league at top 5 positions and Manchester United wins the Europa league.
Of course it's possible to see 7 premier league teams in the champions league next season but only if Manchester United and Aston Villa should win the Europa league and the Champions league as you said. I don't think it's impossible it is only difficult to see it happen as the both teams don't have a consistent performance recently and they cannot be relied on. The chances of Manchester United winning the Europa league is higher than Aston Villa winning the champions league so the chances of seeing 7 premier league teams in the champions league next season is pretty low.
This is very funny sha, Aston villa win championship league people that loss 3:1 against PSG I am not even sure if they will qualify in this quarter finals, before I was hoping they will do something great but I have just confirmed with my eyes that PSG is very good this season and if they should meet Barcelona in the finals they will disturb Barcelona.
It is not impossible to happen in football just that the possibility of it happening is very slim. You are misunderstanding his point, he is not saying Aston Villa will win he is just making assumptions that if Villa should eventually win then we will see 7 premier league teams in the champions league next season. If Arsenal wins it and Manchester United wins the Europa only 6 teams will be in the champions league.