With Karim Benzema, Marco Asensio, Eden Hazard and Mariano Diaz all set to leave the club, Real Madrid are expected to be active in the summer transfer window.
They will be keen to strengthen in attacking areas, while their midfield could be bolstered by the addition of Jude Bellingham.
However, Los Blancos may also need to recruit a new left-back amid uncertainty surrounding the futures of Ferland Mendy and Nacho Fernandez.
Mendy struggled with injury issues throughout the 2022-23 season, and he may be moved on this summer, while Nacho Fernandez is out of contract at the end of the month.
Real Madrid have already announced the signing of their academy product Fran Garcia, who has spent the last two years with Rayo Vallecano.
Los Blancos could still look to bring in reinforcements, though, and Davies has been identified as a potential target.
According to Marca, Real Madrid have already make contact with Bayern to enquire about the Canadian's availability.
The report claims that Bayern have left the door open to a potential sale, although they are still keen to keep hold of Davies.
The Canada international has two years left to run on his contract, and the Bavarians are looking to tie him down to a new deal.
A recent report suggested that Bayern views his contract renewal as a priority, and as a result, they have opened negotiations over an extension.
The player's agent, Nedal Huoseh, recently admitted that his client is currently attracting interest from a couple of clubs.
"A number of clubs are interested [in Davies] but no direct talks [on a transfer]," Househ told TSN. "Davies has two years left on his contract. Bayern are hoping to extend the contract. Nothing confirmed yet."
Since joining Bayern in the summer of 2019, Davies has gone on to make 152 appearances for the club, registering eight goals and 25 assists.