The Denmark Under-21 international has produced some impressive displays since joining Rovers in September and boss Paul Trollope insists it will be a real tonic to keep Andersen.
He told the club's official website: "They (Reading) have one or two things to look at at their end, but in principal we have agreed to the end of the season, so unless there is any change in circumstances over the weekend at their end, we are hoping that will be completed.
"That will be a big boost for us. Mikkel is very keen to stay and we are of a similar mind set, so hopefully we can get the paperwork done on Monday and he can continue in our goal."
Source: Team Talk