The 25-year-old scored twice against the Hoops for former club Astana in the Champions League qualifiers in August 2017 and was linked with a move to Scotland in November that year, and again earlier this year.
However, Twumasi is set to leave Alaves in Spain to join Turkish second-tier outfit Gaziantepspor after struggling to settle into life at the Mendizorrotza Stadium, making fewer than 15 appearances mostly as a substitute.
The versatile attacker, who can operate as a centre-forward or on either flank, first came to Europe with Latvian side Spartaks Jurmala, before joining Astana on loan. He then moved to Russian side Amkar Perm, again on loan, before a second temporary spell with Astana ahead of a permanent move.
He joined Alaves in a £3 million deal last summer, signing a contract until June 2022.