Rangers are hoping to finalise the appointment of a new manager before the international break ends.
The Glasgow giants conducted interviews with several candidates last week before making a final shortlist of targets.
Clement held conversations with Rangers despite also having suitors from the Middle East who are also pushing to sign him.
The ex-Monaco coach is now the leading contender to become the next Rangers boss following talks.
Rangers are yet to make a final decision but they have been left impressed by the Belgian following interviewing him.
Former Rangers defender Kevin Muscat, who also spoke with the club, is still in the race for the Gers job.
Lampard and Scott Parker were considered as well but Rangers are not proceeding with either of them.
A final decision is expected to be made in the coming days as Rangers mull over who to finally go for.
