Bayern and Davies are currently at odds over a new deal, as the recently dethroned German champions have been attempting to tie him down to a renewal without success.
The left-back's wage demands are believed to be too excessive for Bayern to bow to, and he can therefore leave the club for nothing in just under 12 months' time.
Reports claiming that Davies has already verbally agreed a switch to the Bernabeu have been denied by the defender's agent, but Carlo Ancelotti's side are understood to possess a serious interest in him.
Bayern have not yet conceded defeat in their efforts to keep the 23-year-old at the Allianz Arena, though, and they would still be due a fee if Real try to bring him to the Spanish capital this summer.
Real Madrid 'refuse to fork out Bayern asking price'Thanks to Bayern and Real's respective Champions League quarter-final wins over Arsenal and Manchester City, Davies will square off with the La Liga leaders in the semi-finals, potentially meeting some of his future teammates.
According to Sport, though, Real Madrid may delay their pursuit of the Canada international for financial reasons, as Bayern would supposedly demand between €50m (£43.1m) and €60m (£51.8m) to sell him this summer.
With Real Madrid not willing to go north of €40m (£34.5m), the Spanish giants would be happy to wait until 2025 to sign Davies on a free transfer, allowing them to focus their efforts elsewhere this summer.
The Canadian would arrive in the Spanish capital as a successor to Ferland Mendy, whom Ancelotti supposedly believes is the best
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