England wing-back James is understood to be close to completing a new long-term deal to stay at Stamford Bridge, with talks on a similar extension for Mount thought to be progressing positively too.
Real Madrid have had James in their sights as a long-term target, but the Bernabeu giants will see any current designs on the 22-year-old thwarted by Chelsea securing a new deal for one of their brightest talents.
Chelsea spent more than £270million in a record transfer window spree, with Pierre-Emerick Aubameyang the final high-profile addition on Thursday.
The Blues' former assistant boss Morris hailed Chelsea's new owners Todd Boehly and Behdad Eghbali for "working in tandem" with manager Thomas Tuchel amid a wide-ranging squad overhaul.
But the former Blues midfielder considers new terms for James and Mount as the most vital moves for the club.
"It looks like the manager and the owners are working in tandem, and that's important going forward," Morris added.
"The new owners are backing the manager and that's big, especially with some big and important signings coming through the door.
"But when you're looking at the two most important signings, for me it would have to be seeing Mason Mount and Reece James tied down to new long-term deals.
"They are the first names on the team-sheet and they need to be tied down, and I think that's got to be what they are looking at next."
James' deal expires in 2024 with Mount's existing terms running until 2025.