The Premier League duo are believed to be keen on the current Paris Saint-Germain coach, with the futures of Roberto Mancini and Arsene Wenger far from certain.
However, reports have emerged that the Italian has reached a verbal agreement with Real to take control at the end of the season, when Jose Mourinho is expected to leave.
Despite guiding the nouveau riche Parisians into the last-16 of the Champions League and to the pinnacle of Ligue 1, Ancelotti is thought to be on the verge of leavng the Parc des Princes.
PSG’s Qatari owners are thought to be keen to draft in a big named manager as they look to expand their global image both on and off of the field.
Mourinho has been mooted as a possible candidate, and could complete a straight swap this summer.
Ancelotti enjoyed a successful stint at Stamford Bridge, guiding the Blues to the double in 2010, before being sacked 12 months later.
Both City and Arsenal were thought to be in the race, but Ancelotti, who doesn’t have an agent, is rumoured to have ‘shaken hands’ with Real.