Johnson is keen to leave City in order to get regular first-team football.
The 25-year-old has also been linked with the likes of Sunderland, Spurs and Everton.
But the Independent reports that Liverpool have emerged as favourites to land the highly-rated England international.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.