Sheffield United could still receive funds in return for Ismaila Coulibaly in the summer.
The Malian left Bramall Lane last week as he made a move to Allsvenskan side AIK on loan.
However, he is hoping to play regular football and then earn a permanent move.
Givens the Blades have an option to extend his contract by a year, he cannot leave on a free.
Thomas Berntsen, AIK's sporting director, told Fotbollskanalen: "I am very happy. Ismaila is a good player that competes with many others. He is useful, at a good age and motivated.
“It will be good. He is an all-round player who is good in the air, good with the ball and he scores goals. It will be exciting to see where he plays. Whether he plays is entirely up to him.
“We have a very good dialogue with Sheffield, so if Ismaila likes it, it may very well be that he stays longer."