The Gunners were one of the busiest clubs in the Premier League during the summer transfer window after Emery completed six deals.
Elneny and Mustafi have fallen down the pecking order at Arsenal following the new arrivals.
The Germany international has been linked with a potential move to Ligue 1 side AS Monaco but a deal has failed to materialise so far.
However, Arsenal manager Emery has now reiterated that he wants both Elneny and Mustafi to seek new challenges and leave the north London outfit.
“We now have some players who know their situation,” Emery is quoted as saying by Metro.
“For example, Elneny and Mustafi know their position in the squad and I really want the players to be happy here, I want them to be protagonists.
“Last year with Mustafi and Mo, when they didn’t play they weren’t happy.
“I spoke with them a lot of times last year and in pre-season, and I think it is positive for them to leave and sign for another team where they can be protagonists, be happy and continue their careers.
“They are very big players but for one circumstance or another, they are going to have less chances to show their capacity or to be happy with us and the minutes they play in matches.
“But they know the situation and really, really I am wishing the best for them – and I think now the best for them is to be protagonists in another team, to sign and get another challenge with another team.
“We respect them, and they are training with us, but they know their situation.”
Arsenal signed Brazilian teenager Gabriel Martinelli and Saint-Etienne’s 18-year-old William Saliba to prove Emery has one eye on the future.
The Gunners bolstered their midfield option with the loan signing of Spain Under-21 international Dani Ceballos from La Liga giants Real Madrid.
Arsenal smashed their club record to sign Ivory Coast international Nicolas Pepe from Ligue 1 side Lille to bolster their options in wide areas.
The north London side concluded their summer transfer activity with the addition of Celtic full-back Kieran Tierney and Chelsea FC centre-half David Luiz.
Arsenal will return to Premier League action next Sunday with a home clash against derby rivals Tottenham Hotspur.
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