The Spanish giants were unsuccessful in their first bid of €160million (£137m) for the French superstar striker earlier this week but are confident of securing the deal with a second approach.
It is claimed that Madrid will be able to land the 22-year-old in a €170million deal plus a further €10m in add-ons in a deal that they have long been planning to complete.
A report in Diario AS outlines that Real Madrid plan is to hand Mbappe the number 5 shirt at the club – made iconic by Zinedine Zidane in the early 2000s.
The number is currently held by central defender Jesus Vallejo, who has returned to the club from various loan spells away and is unlikely to be a regular first-team starter this campaign.
Real Madrid plan to ask the defender to relinquish the shirt but if that cannot be done for this year, Mbappe could take the free number 19 shirt and inherit the number 5 kit in future seasons.