Canos shone in last season's Championship
The same publication reported earlier in the week that Canos was set to join the Robins, whose £2.5 million had been accepted by the Reds.
However, alleged interest from recently relegated Norwich is said to have prompted the Spaniard to stall over his potential exit.
Robins boss Johnson wants Canos at Ashton Gate
Canos spent last season on loan to Championship side Brentford, impressing. However, the 19-year-old's apparent £10,000-a-week wages demands are said to have scuppered his chances of a permanent move to Griffin Park, while an agreement with Liverpool could also not be reached.
And that prompted Bristol City, who avoided relegation following Lee Johnson's February appointment, to launch a move for Canos in the meantime - offering, reportedly, a sizeable sell-on clause and buy-back option.
Redmond has left Norwich to replace Mane at Saints
But the sale of England Under-21 star Nathan Redmond to Southampton - who replaces, ironically, new Liverpool signing Sadio Mane on the South Coast - and anticipated exit of Ireland ace Robbie Brady to Leicester City means Norwich are also in the market for a new wide man this summer.
Liverpool's Canos in action with then-Everton defender Sylvain Distin