The South Korea international is due to spend the remainder of the 2013/14 campaign at the Stadium of Light after being deemed surplus to requirements at Swansea City.
He has, however, remained evasive when it comes to the subject of his future - with Swansea having parted with the services of manager Michael Laudrup to suggest there could still be a role for him in South Wales.
Poyet hopes that will not prove to be an issue when he heads for the negotiating table this summer, with there a desire on his part to bring the highly-rated midfielder onto his books on a full-time basis.
He told the Sunderland Echo: "I think the important thing is how happy Ki feels when he plays for us. How much he is enjoying his football here?
"Being realistic, he is still under contract to Swansea.
"Now Swansea have changed their manager and who knows whether whoever comes in will want Ki or not want him. We will have to manage that situation.
"But if you ask me if he is a player I would like to have here, yes I would."