The Iceland international is expected to officially complete his switch to Goodison Park at some point on Wednesday evening, bringing an end to one of the longest running transfer sagas of the summer.
It has been widely reported that Everton have agreed to pay Swansea £45m for a player who played a direct part in 22 Premier League goals last term.
Speaking to reporters on Wednesday afternoon, Koeman said: "The latest is he had his medical this morning. What I heard was there was no problem. I have seen him in blue but I don't know if all the paperwork is done."
Sigurdsson will not feature in the Toffees' Europa League qualifier against Hajduk Split on Thursday night, but he may be used in next Monday's league clash with Manchester City.