Sky Blues boss Chris Coleman has revealed he may possibly look to sign the 23-year-old permanently at the end of his loan spell, but any decision over his future remains in the hands of Albion chief Roberto Di Matteo.
As for Barnett himself, he is just focused on getting as many minutes on the pitch as possible after a knee operation towards the end of last season.
Speaking about City's interest, he told the Coventry Telegraph: "It is pleasing to hear but we will just have to see what happens and you never know what could happen between now and January. I am trying to keep my options open, get as many games as I can and try to help the boys here push up the table."
Meanwhile, Joss Labadie has returned to West Brom after his loan spell was cut short by Shrewsbury boss Paul Simpson, who was "disappointed" by the midfielder's attitude to training and matches.