I see Manu as the strongest candidate for Osimhen. Chelsea did not buy players for such astronomical amounts after Abrabomovic left the team. I don't think they can either.
Arsenal or Manu can buy him. Manu is the strongest candidate because they have had terrible seasons in recent years.
Manchester United have not even shown serious interest in Osimhen and even till now they're not really focused on him. There main focus for now and Gyokeres. They belive the influence of Amorim can convince him to join Manchester United. I don't see that happening if they don't make it to the champions leagues.
But what do you mean Chelsea have not made such big signing since Abramovic left? The same Chelsea that signed Enzo for 100 million or the Chelsea that signed Caicedo for 100 million? Which of them? the Chelsea that signed Mudryk for 89 million?