Abramovich is unlikely to flinch at the world record bounty needed to lure the best player on the planet to London if it helps to secure Conte's immediate future at Stamford Bridge.
The Russian's next move is likely to be the key in a week that will almost certainly see football's astonishing spending spree soar through the roof.
Ronaldo set the ball rolling by revealing plans to quit Spain over tax fraud allegations, a decision that has alerted suitors all over the footballing globe.
Cristiano Ronaldo is targeted by Roman Abramovich, who could use Eden Hazard as payment
Chelsea's canny backer will bank on even just an interest in Ronaldo would help allay Conte's fears about the club's summer transfers commitment, and heal increasingly damaging divisions over his text sacking of firebrand striker Diego Costa.
But whatever move Abramovich makes he will face fierce competition for Real's wantaway superstar from a host of top clubs as far afield as China, America, Europe - and Manchester United in particular.
At the end of the day, though, it is unlikely to be money that will talk because Ronaldo has plenty of that with a BILLION dollar fortune already stashed away.
Suggestions by his sister, Katia, that he has recently fathered twins with a surrogate mother in America - and the future of his closely guarded son, Cristiano Jnr - will also be a major consideration in where he next plays his football.
Cristiano Ronaldo stunned the football world when he reportedly declared he is ready to quit Spain
The 32-year-old, who is intensely private about his personal life, will also have to be convinced that any children are protected from the glare of publicity he is constantly subjected to.
That is also one of the reasons why the bookies are making his old club, Manchester United, favourites to sign him again - even though they would want Wayne Rooney off the wage bill to accommodate him.
Ronaldo enjoyed a very successful relationship with his then manager, Alex Ferguson. And his mother, who plays a major role in Cristiano Jnr's upbringing and welfare, likes the city and would not be too far away.
In the meantime, however, the world's big spenders are now falling over themselves to splash out on a player who would cost them a record £150million. At the very least.
That is the fee Real are understood to be prepared to settle for, even though Ronaldo, who signed a new £365,000-a-week deal only last November, is understood to have a £870million buyout clause in his contract.
Real President Ramon Calderon has already been talking to United about selling striker Alvaro Morato to them. In turn he wants to buy the Reds goalkeeper David De Gea.
All of which means the scene could be set for a record busting deal that could end up costing United close on £200million.
Unless Mr Abramovich bursts their bubble, that is!