Neither the Italian nor the Ghanaian has tallied a single goal or assist through a combined 34 Serie A appearances this term, leaving the Viola and Rossoneri ready to move on.
Aquilani’s former representative told Lady Radio in March that there had been no movement on a possible extension, a scenario always looking unlikely in kind for Essien.
Each midfielder is presently in the top five earners for his club and with the season wearing down, it appears Fiorentina and Milan are keen to be shorn of their considerable wages.
The question is where to next – with Aquilani and Essien each in the latter stages of their careers, they are seemingly prime candidates for alternative destinations.
And agent Andrea D’Amico told Sportitalia that MLS is a possibility for the Italian: “Aquilani is a top player. He’s a player with a great record.
“I haven’t spoken to anyone, but I’m sure we’ll get a satisfactory outcome, a high-level project, whether that’s in Italy or abroad.
“MLS, where [ex-Juventus forward Sebastian] Giovinco now plays will soon be an important league, with all the multimedia communication which we’ve neglected.”
Meanwhile, Tuttosport claim that New York Red Bulls and Orlando City have eyes for Essien, with his former Milan team-mate Kaka currently plying his trade for the latter.
Aquilani and Essien have experienced differing fortunes in the aftermath of their Premier League careers, the former having truly never settled in England.
The Roma youth product failed to live up to expectations on Merseyside but was a productive performer for Juventus, Milan and Fiorentina upon returning to Italy.
Competition for minutes in midfield and his approaching 31st birthday have seen a dip in his form for the Viola this term, setting up his likely departure.
Essien’s glittering career at Chelsea was brought to an end in January 2014 after it had become clear injury issues down the years had sapped his effectiveness in the centre of the park.
The 32-year-old has made just 10 Serie A starts since arriving at San Siro 15 months ago, living through a difficult period at Milan in which there has been little stability.