Thiago Silva and Jorginho are both wanted by Thomas Tuchel for the long term.
The Blues pair both started Tuchel's first match in charge at Stamford Bridge on Wednesday.
Reporter Gianluigi Longari claim Chelsea are trying to tie Jorginho down until 2025 and Silva until 2023.
Jorginho signed for the Blues on a five-year deal in 2018, meaning his current contract expires in 2023.
The German's love of a passing metronome in midfield could see the Italian's Chelsea career reignited.
Silva, meanwhile, left Tuchel's Paris Saint-Germain on a free transfer last summer and was brought in by the Stamford Bridge outfit on a one-year deal with the club having a 12-month extension option.
As early as November, Chelsea were linked with triggering their extension clause for him.
There was a suggestion that Tuchel and Silva fell out at the end of last season, especially when the centre-back labelled his former boss' sacking at PSG ‘predictable'.
However, both camps insist there is no problem and in fact Tuchel wanted the veteran Brazilian defender to stay at the Parc des Princes.
This article was most recently revised and updated 2 years ago