The Englishman was concerned he may be moved on in the summer as part of manager Pep Guardiola's clearout.
According to The Sun, talks with Guardiola have led Walker to believe he is wanted at the club.
Walker got in trouble during the COVID-19 lockdown for having prostitutes over at his home.
But a source - quoted by The Sun - has said: "Pep put his arm around Kyle during the lockdown. They have become very close.
"He has become a bit of a father figure to him throughout this whole period and they have bonded."