Ozil, 24, joined Premier League side Arsenal for 50 million euros on Monday's transfer deadline day after Real completed the signing of Gareth Bale from Tottenham Hotspur.
The Brazilian was also said to have taken a significant pay cut to facilitate his move to the San Siro, accepting an annual salary of four million euros plus bonuses, a considerable reduction from the 10 million euros a year he received in Madrid.
Arsenal and Manchester United are expected to be busy in the transfer market Monday. English clubs are already close to spending 500 million pounds ($775 million) in the summer window.
The 32-year-old Argentina international is renewing his ties with City's Chilean manager Manuel Pellegrini, the pair having worked together at both River Plate and Malaga.
No firmer details were given in the report, although speculation suggests Real could release Kaka for free or allow him to go on a two-year loan.
Bale has signed for an undisclosed fee and will be presented to the media and the club's fans on Monday afternoon after undergoing a medical.
Kondogbia, who left Lens for Sevilla a year ago, made his debut for France in their 0-0 friendly draw in Belgium a fortnight ago having won the under-20 World Cup with Les Bleus in July.
Kaka has never really settled in Madrid and remains unhappy despite his former Milan coach Carlo Ancelotti now being in charge at the Santiago Bernabeu.
The 26-year-old German-born Ghanaian international started his career in the Bundesliga with Hertha Berlin, his hometown team, in 2005.
Eto'o previously worked under Mourinho at Inter Milan and was a member of the team that claimed an unprecedented treble of Serie A, Coppa Italia and Champions League titles in 2010. Willian and Eto'o are among a number of players to have been moved on by Anzhi after the Russian side's billionaire owner Suleiman Kerimov decided to restructure the club and drastically...