Karlsson moved to the Black Cats last summer, but after being limited to just one first-team appearance, Jonsson has insisted that his client isn't prepared to wait for his chance at the North-East club.
Jonsson told The Journal: "What David wants is to find a club that would have him as they see him, as the offensive player he is. The problem lies in that Sunderland must take a loss. They do not want to sell him cheaply.
"We can get a loan, but we're not so keen on it. I do not think that David wants to be loaned out again. We want to find a permanent solution so David gets peace and quiet for a while."
The 20-year-old was loaned out to Kilmarnock for the second half of last season, but he only made four appearances for the Scottish team.