According to a report from Relevo journalist Jorge Picon (as captured by @iMiaSanMia), Real Madrid is still contemplating a move for Bayern Munich left-back Alphonso Davies:
Real Madrid have not completely closed the door on Alphonso Davies this summer and are preparing a final attempt to try and sign the player this month. Real will likely bid for Davies in the final days of the window so that Bayern are left with the decision either to sell or risk losing him for free 10 months later.
The Spanish side will only pay what they consider Davies is worth considering his contract situation. If Bayern ends up rejecting the offer, Real will go back for the Canadian next year, where they are optimistic about signing him on a free transfer.
Abendzeitung journalist Maximilian Koch (via @iMiaSanMia) also issued an update and said that Bayern Munich will not improve the last proposal it made to Davies for a contract extension. With that, a transfer could still be in play:
Bayern have decided not to improve their contract offer for Alphonso Davies anymore. The player can decide after his vacation whether to take it or not. A move this summer is still possible.
For Bayern Munich, the club has already bolstered the left-back position in some respects. On the current roster, Hiroki Ito, Raphaël Guerreiro, Adam Aznou, Josip Stanišić, and Noussair Mazraoui all have experience playing the position.
There are issues within that group, though. Ito suffered an injury last week that is expected to keep him out two-to-three months, Guerreiro missed 23 games due to injury last season, Aznou is still very green, Stanišić is more of a right-back / center-back, and Mazraoui could be sold at at any moment to Manchester United.
If Davies leaves, it will be interesting to see if Bayern Munich adds another player into its left-back group.