The two academy graduates have just played key roles in helping the Blues secure sixth place in the Premier League standings, a position which they hope will lead to Europa League football.
That qualification is dependent on whether Manchester United overcome Manchester City in the FA Cup final on Saturday and if Chelsea can comply with the Premier League's and UEFA's financial regulations.
In the short term, though, co-owners Todd Boehly and Clearlake Capital are focused on finding a suitable successor for Mauricio Pochettino, who left his role as head coach last week.
Pochettino and the West Londoners are said to have reached the mutual decision to go their separate ways, a consequence of it being deemed that the Argentine was not the right fit for Chelsea's preferred structure.
While Chelsea's hierarchy will be hopeful that the move will prove productive, there are two first-team players who are seemingly closer to the exit door.
Gallagher, Chalobah less likely to stay
According to the Evening Standard, Pochettino's departure on Tuesday will not have helped the cause of Gallagher's and Chalobah's.
Pochettino has always talked up the influence of Gallagher, who has been his captain for large parts of the season due to injuries to Reece James and Ben Chilwell.
The 24-year-old missed just one Premier League game all season, due to suspension, and contributed five goals and seven assists during an influential campaign where he convincingly won over the club's supporters.
Meanwhile, Chalobah went from being injured up until February to playing a key role at centre-back or right-back, Chelsea not losing any of the 10 Premier League games that he started.
Nevertheless, the report indicates that Chelsea plan to proceed with trying to attract the biggest offers possible over the coming weeks, the aim being to sell the homegrown pair before June 30.
Chelsea squad have concerns over possible exits
Pochettino was said to be ready to battle to keep both players at Chelsea, and it is alleged that their teammates do not want to see either Englishman leave.
Gallagher and Chalobah are regarded as model professionals whose impact will be felt in the dressing room should they follow Thiago Silva out of the door.
Both players are eager to remain at Stamford Bridge, yet it appears that Boehly and co will push for their exits, even with Chalobah having four years left on his contract.
Compatriot Gallagher has just the one, and the scenario remains that the England international could enter the final year of his contract if he does not find an alternative club to his liking.