Liverpool signed Diaz, 25, for an initial fee of £37.5 million on Sunday but ran out of time to complete a deadline-day deal for Carvalho. Klopp said the club would be "crazy" not to retain an interest in the highly rated teenager, who is out of contract at the Championship leaders at end of the season.
"Our strategy is to sign the right players at the right moment," the Liverpool boss said on Friday. "We recognise issues like a position or contracts. We are long together with this team, it's a fantastic team, one of the most successful in the history of this club but we will never miss having a look ahead and that's exactly what we are doing. We are Liverpool so we cannot only work with talents and say: 'Let's have a look in two or three years and they will be ready'".