Liverpool have been strongly linked with the defender.
The Reds have been strongly linked with Leicester City left-back Ben Chilwell - with the Mirror's report also saying they have had a bid turned down by the Premier League champions for his services and have moved their attentions elsewhere.
Alberto Moreno is the current left-back of choice at the club with Brad Jones the notable deputy, but both Jon Flanagan and Joe Gomez have shown they can play on the left side of the defence if required.
Moreno has been criticised pretty frequently for some defensive gaffes, notably in the Europa League final, and that is an area of the field that Reds boss Jurgen Klopp seems keen to address, although it looks as if he is looking for a defender to compete with the Spaniard rather than replace him from the start of the new Premier League season.
No reason was given in the report for the Reds' cooling their interest on Hector, but it is apparent that Liverpool really need to strengthen in that area.
Any hope Hector making the move from Cologne this summer to Merseyside appear to be extinguishing but it will be interesting to see if Klopp manages to land a left-back this summer, and what it will mean for Moreno's starting opportunities at the club come the start of the season.