Andre Villas-Boas, the new Chelsea manager, is keen to improve the quality available to him on either wing, and has sanctioned an approach for the England winger.
Though width is fundamental to Villa-Boas's tactical planning, his squad is not considered especially well served in the area.
Florent Malouda, the team's most productive wide player in recent seasons, has been offered to a number of Serie A clubs to raise transfer funds.
Johnson, 24, is capable of playing on either side of the pitch and also provides a goal threat.
Being English, he would also help Chelsea comply with the Uefa and Premier League regulations that restrict the numbers of non-home-grown players.
Though Johnson has failed to convince Roberto Mancini to install him as a regular starter since his £7 million (Dh42.1m) recruitment from Middlesbrough in early 2010, City are extremely reluctant to sell to a title rival.
Johnson is understood to be open to a move south but the Abu Dhabi-owned club are not expected to change their position.
Chelsea have yet to add a player with significant first-team experience to their ranks in the current transfer window.
Earlier in the summer they were unsuccessful with an informal approach to Arsenal's Theo Walcott, another England winger.
Villas-Boas yesterday acknowledged that he knew he would have little time to settle in at Stamford Bridge and that immediate success was expected from him.
He said: "It's pretty straightforward what you have to achieve at this club isn't it?
"You have to win trophies. If you have big success and you know the hunger of what these players want to achieve, I think it is straightforward, you have to challenge for the Premier League and also the other trophies and I see no reason why this cannot happen.
"You can see a pattern in the last four years in the Champions League: the semi-finals, Chelsea have been present. It's just one more step.
"Will I be able to do it in the three years I have a contract with, or one or two, I don't know. It's a challenge that we want to take."