The 25-year-old England international is expected to leave City on loan this summer.
Johnson has fallen down the pecking order at the Etihad and is expected to be keen on regular first-team football.
Metro reports that Fulham are also reportedly keeping tabs on the winger.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?