Summary:
Lampard really wants Declan Rice for his personality as well as talent, rare that someone so young has the natural authority to captain a PL team. However, he cannot be signed for the quoted 80m figure without additional player sales.
Talks have been held with Brighton over Lewis Dunk who is a natural leader that would help with defending crosses and set pieces.
Dunk has an understanding with BHA that he can leave if an acceptable offer is received from a top6 club, but what that offer needs to be isn't very clear. At this stage a deal is still unlikely (as talks were very preliminary) and it would be cheaper to sign Ben White instead but he is totally unproven in the PL.
Thiago Silva has been offered to Chelsea but it would be a surprising deal for Chelsea to do because he would be the oldest outfield signing of the Roman Abramovich era.
His lack of speed at this stage of his career would make him ill suited for playing in Lampard's high pressing system. Unai Emery blamed him for dropping too deep in the infamous 6-1 defeat to Barcelona because he feared his athletic limitations would be exposed.
Silva has leadership credentials but he has tasted failures both for the national team (World Cup 2014) and multiple Champions League runs where he wasn't exactly a source of inspiration.
Chelsea know they need a centre back and will push for Rice but might turn attentions elsewhere if a deal isn't possible.