The 24-year-old, who has been in Thailand on duty with a Danish league select team, expects that to be completed soon and he is keen to sort personal terms with the Glasgow club.
"This is a dream I have had for a long time," Rasmussen said in the Mail on Sunday.
"It is a step up for me, if it becomes a reality. I expect a clarification on Monday, but now I am going home to Denmark with the rest of the league team.
"I have not even negotiated my personal things, but if the other things go in order, then I guess this also will. And I would really want it to go in order."