Canos, 19, has been offered a new deal the report claims, describing the situation between club and player as a 'stand-off'.
While money, length of contract, and playing time will be determining factors, Canos' comments after making his debut at the weekend gave no indication he was looking to move on.
The teenager even vowed to be back at Liverpool for pre-season raring to go, desperate to make a further imprint on the first team.
He told the Liverpool Echo: "It’s been the best season of my life. I made my debut in the Championship, I scored my first professional goal and now I’ve made my debut for Liverpool. I am really happy.
“I’ll be back for pre-season and ready to go 200%.”
After a campaign on loan at Brentford he has had a taste for first team football, and will have a chance and a fresh slate to try and impress Jurgen Klopp in pre-season.
The contract situation could hamper this, but Canos' preference certainly seems to be to stay put and try and make it work for now, but come August if he is nowhere near the first team set up, then it may be time to reconsider his next move, which is where Rangers could come in.