This Morning's Times claims Abramovich met with Kaka and Bosco Leite, his father and agent, in Milan last week.
Kaka, the former Fifa World Player of the Year, is expected to leave the San Siro this summer, but Abramovich was reportedly told that the Brazilian prefers a move to Real Madrid.
Florentino Pérez has returned to the Bernabeu as president, and reports in Spain claim Real could announce Kaka's £60 million signing this week. That fee would world record £45.6 million they paid for Zinédine Zidane eight years ago.
Ancelotti is understood to have recommended that Chelsea sign Andrea Pirlo, but it is unclear whether Milan owner Silvio Berlusconi would permit the Italy international to leave.
Yuri Zhirkov, the CSKA Moscow forward, is expected to join Chelsea over the summer, and captain John Terry believes more top players will follow him.
'I think we'll see Chelsea back and competing for the top players,' said Terry . 'I think there'll be many players we'll be in for in the summer, but when big players come up. We need to show people and let them know that, yes, Chelsea are back.'
Speaking about Ancelotti, Terry said: 'I think a few of the backroom staff have worked with him before, and Sheva [Andriy Shevchenko] as well. He speaks very highly of him. If he's the man to come in, he's got a great bunch of lads to work with. Knowing him and knowing us, it could be the start of something very good.'