The France World Cup winner only left Atletico Madrid last summer for Bayern, but is now being lined up for an immediate return to the Spanish capital.
Real, reports Le 10 Sport, will push Bayern to open talks about a deal for Lucas in the coming weeks.
Real see Lucas as a replacement for veteran wing-back Marcelo and to provide competition to Ferland Mendy.
Real coach Zinedine Zidane is convinced by Lucas' quality and has approved the move.
Lucas left Atletico last year after Bayern agreed to meet his €80m buyout clause.