Tottenham and Chelsea are monitoring Atalanta defender Giorgio Scalvini, valued at £42m, though Spurs have already added centre-backs this summer.
Spurs may not be finished in midfield, with talks under way for a third addition as their summer rebuild continues.
Spurs beat Chelsea 2-1 despite Kevin Danso's red card. Ben Davies, Antonin Kinsky and Richarlison were highlighted, while Andy Robertson was criticised for Chelsea's goal.
Tottenham are among the clubs monitoring Ferran Torres as his Barcelona contract talks stall, with Arsenal also linked to the forward.
Roberto De Zerbi said he does not know if Richarlison will stay, despite calling him important after his winner in Spurs' 2-1 pre-season win over Chelsea.
Spurs have made an approach for a Premier League striker who scored at Tottenham Hotspur Stadium last season and received a swift response.
Tottenham and Arsenal are scouting Chivas winger Hugo Camberos at the CONCACAF U20 Championship as they weigh a move for the 19-year-old.