The transfer was thrown into doubt as FIFA regulations forbid a player from appearing for three clubs during the course of a season.
Cousin, 30, played 20 minutes for Lens this season before a £1 million move to Ibrox in August, but is hoping to win dispensation to allow him to complete his dream move to England.
Rangers have been linked with Aston Villa striker Luke Moore as a possible replacement but manager Walter Smith insists any dealings in the transfer market do not depend on the sale of Cousin.
"If we found the player we wanted, the money was available for us anyway," he said. "It wasn't the fact that we had to transfer anyone to get the money. The funds are available if we can come up with the right people.
"When someone comes along and asks if they can take one of your players, we have a decision to make. We agreed the fee and I decided that we could let him go. We would only go into the transfer market if we could find someone I felt could improve the squad rather than taking someone for the squad.
"At this stage of the season, it's not always easy to find a player of that kind of level because clubs obviously want to keep their good players for the remaining part of the season.
"So, unless we find someone who I feel will improve the team, I'm happy to go with the squad we have."
