England Under-21 international Mount spent the 2018-19 season playing under Lampard at Pride Park on loan, making 44 appearances, scoring 11 goals and providing six assists in all competitions.
The 20-year-old's current deal at Stamford Bridge expires in less than two years, but the appointment of Lampard has helped convince Mount that his long-term future is in west London.
Goal can confirm that talks have already begun regarding the terms of the deal despite Mount being on holiday after representing England the U21 European Championships in Italy in June.
The presence of Lampard's assistant manager Jody Morris, who worked with Mount when managing the Chelsea Under-18s squad, has also proven pivotal in convincing a player who joined the club at the age of eight.
Joe Edwards, who also worked with Mount during his time in the club's academy, is being promoted from his role as coach of the club's Under-23s Development Squad to Lampard's backroom team as the club begin to focus on bringing through their most talented youth products.
Tying down homegrown talent is likely to form the basis of Chelsea's off-field work over the summer with their FIFA-imposed transfer ban meaning strengthening their squad from the outside is not possible until the summer of 2020.
Ruben Loftus-Cheek is set to sign a new £120,000-a-week deal with his boyhood club, with the announcement on that expected imminently.
Chelsea are also keen to tie Callum Hudson-Odoi to a fresh five-year deal, with talks ongoing with the 18-year-old and his representatives.
Confidence is growing inside the club that the England winger will remain in west London after they rejected Bayern Munich's advances during the January transfer window.
Should they fail to agree terms on a fresh contract for Hudson-Odoi, however, then he would be able to leave on a free transfer at the end of next season when his current deal comes to an end.
Following the confirmation of Lampard's appointment on Thursday, the ex-Blues midfielder will oversee the return of a number of his players for pre-season training on Friday before the squad fly out to Ireland for their first friendlies of the summer.
They then begin their Premier League campaign against Manchester United at Old Trafford on August 11.