It’s understood that City have had an offer for Barry accepted and are now offering the Aston Villa captain a big wage increase to entice him.
Meanwhile Argentine striker Ezequiel Lavezzi – who has been linked with a move to Anfield this summer has strongly hinted that the time has come for him to leave Napoli.
Lavezzi wrote an open letter to the fans of Napoli explaining that although he wants to stay at the Serie A club, club officials have treated him badly in recent contract negotiations.
Manchester Utd are also said to be interested in 24-year-old Lavezzi, who has an estimated value off around Â£12million.
His agent, Alejandro Mazzoni, told Sky Italia, “There is a very real offer from a team who are playing in the Champions League and where he would earn much more than here.”
And Reds winger Yossi Benayoun has revealed that there have been inquiries made into his availability since the end of the season.
Benayoun flourished in the second half of the season for the Reds, scoring vital goals on their pursuit of the Premier League title. But the Israeli international admitted that competition for first team places at Anfield could force him to reassess his situation.
He said, “At the moment, I am a Liverpool player, and unless something surprising happens, I will remain one. But after such a good season, I have had some offers from England and Spain.
“You have to give that some consideration, so there will probably be some discussions with Liverpool.
“I have had a great two years at Anfield and enjoyed every minute. I have long since accepted that, with one or two notable exceptions, there is no such thing as an automatic choice at Liverpool.”
“Unless you are Steven Gerrard, you are going to sit out one or two games, but that is no problem. Stevie is exceptional, and the rest of us accept that.
“The good thing is, I have been playing more, and I hope it continues that way. To be honest, it could be Real Madrid knocking on my door, and I would still rather stay at Liverpool four more years.”