The summer window doesn't close until September 2 in most of Europe's major leagues. Emery recently spoke to reporters and suggested his side are open to selling the pair:
"They are very big players but for one circumstance or another they are going to have fewer chances to show their capacity or to be happy with us and the minutes they play in matches.
"Last year when they didn't play they weren't happy. I spoke with them a lot of times last year and this pre-season.
"I think it's positive for them to leave, sign for another team where they can be protagonists and be happy and continue their careers."
The former Valencia and Sampdoria star—who joined Arsenal in 2016—has seen his reputation plummet in the Premier League over the past season or more.
The Guardian's Chris Godfrey recently joked about his determination to stay in north London:
Mustafi has established something of a cult status in England. He attracted widespread attention for his defensive form during the 2018-19 season, most notably when Crystal Palace beat the Gunners 3-2 at the Emirates stadium in April.
Wilfried Zaha and Christian Benteke each exploited Mustafi's errors to collect a famous win over the Gunners, after which Emery defended his player and insisted he was "consistent" despite repeated mistakes.
The Mirror's John Cross referenced Arsenal's interest in Zaha earlier this summer, joking the Eagles would be wise to swapping Mustafi in part-exchange:
Emery is yet to hand the defender a minute of playing time this season.
Elneny, 27, has failed to figure prominently for Arsenal at any point since he joined from Basel three years ago. Emery hasn't played him much since he replaced Arsene Wenger as manager in 2018, making only 17 appearances in all competitions.
Joe Willock, 20, has started each of Arsenal's league games so far this season and appears to be in the boss's first-team plans, while loan signing Dani Ceballos will provide more strong competition in midfield.
Finding a suitor willing to meet Arsenal's valuation could prove trickier in the case of Elneny. Emre Sarigul of Turkish Football reported earlier in August that Turkish giants Galatasaray were interested:
Turkish Football @Turkish_Futbol1
Galatasaray are in talks with Arsenal over Mohamed Elneny. Lions official Şükrü Hanedar has been in London over the past few days for several meetings. Arsenal are open to a move but Elneny has 3-years on his contract and Arsenal won't let him go on the cheap. GS push for a loan https://t.co/QdNtCqJrOv
Arsenal have recruited enough this summer that Emery feels content allowing Mustafi and Elneny to leave, though finding the appropriate sales or loan deals for either player is another matter.