At this point, I think Chelsea is confused. They don't know what they want. They didn't go all out for Nagelsmann that is why they lost him. They're looking for a coach that has experienced the EPL and that is not a very good idea. Pep and Klopp never had experience in the EPL before they became the managers of their respective clubs but they both did and doing well.
Potter and Lampard both have a degree of experience with the league but they both failed at Chelsea so what's the point of still[cking to that same philosophy? They also had a chance to sign Luis Erique but they refused because of the same lack of experience in the EPL excuse. They might end up with an average coach if they're not careful.
To me, the Pochettino they want to hire is a wrong decision, but what do I know?
I think the board at Chelsea just took a quick look and immediately decided who would be the right fit to be Chelsea coach and that decision fell to Lampard. But in this context, Lampard is a temporary coach, in which Chelsea gives hope to fans that there will be another coach to handle Chelsea next season. I don't understand why the Chelsea management didn't approach Nagelsmann directly even though he was a pretty great coach when he was with Bayern Munich.
Zidane is also reportedly the coach most wanted by fans to train Chelsea. I think the management should also approach Zidane and have direct talks with him to accept this offer because Zidane is a well-known coach who was very successful while at Real Madrid.
Chelsea must look for a coach who has the characteristics of building a stronger team in the coming season. Because the players currently owned by Chelsea are the good quality players they have brought in in this transfer window.