Acquah, 28, joined the Turkish Super Lig outfit as a free agent after his contract with Empoli came to an end in June 2019.
The dynamic midfielder established himself as a key figure for the team, registering 3 assists and scoring 1 goal in 27 appearances.
The Ghana international has attracted interest from several Italian clubs following his performance in the just ended Turkish football season.
“We have to think about the interests of the country. There are transfer offers from Italy for Afriyie Acquah,” Yeni Malatyaspor president, Adil Gevrek disclosed.
Afriyie Acquah was close to a return Italy by joining Lecce during the January transfer window but the move collapsed after Yeni Matalyaspor decided against cashing in on him.