Diouf is due to join his country's pre-tournament training camp on Monday, ahead of Senegal's first Group C clash with Ghana on January 19 in Mongomo.
However, with Stoke due to travel to Arsenal in the Premier League on January 11, the club hope Diouf's departure can be delayed so he can feature at the Emirates Stadium.
Diouf - who scored a brace in Sunday's 2-0 win over West Brom - has enjoyed a strong start to life at the Britannia Stadium following his move from Hannover in June, and Hughes is hopeful the forward can put off his exit.
"We hope we can keep Mame a little bit longer," he told the club's official website.
"He's due to go on January 5 - we'll ask and see if we can keep him for the Arsenal game but in fairness Senegal are well within their rights to call up him next Monday.
"There's not a great deal we can do about that but we'll have a conversation and see if we can convince them just to give us a little bit more time with him."
