William Gaillard, UEFA's director of communications, said that if Chelsea owner Abramovich has a controlling interest in both he will have to decide which club can stay in the competition, reports Australia’s Fox Sports.
The possible controversy has arisen because Abramovich is a leading shareholder in Russian oil giant Sibneft, which sponsors CSKA.
"We do a superficial check of all clubs to establish that no individual owns more than 51 per cent of two clubs. Where we think there might be a problem we examine the situation more thoroughly."
Chelsea said that UEFA and the Champions League clubs should have no concerns over Abramovich's links with CSKA.
"Mr Abramovich is the owner of Chelsea and Sibneft, a company in which he is one of many shareholders, has a shirt sponsorship deal with CSKA Moscow," said the club's director of communications Simon Greenberg.
"Mr Abramovich has no equity stake nor any direct interest in CSKA Moscow."
He added that Abramovich had no say in how sponsorship money is spent at CSKA.
But Gaillard insists that if there are any doubts, then either Chelsea or CSKA Moscow will not take part in the competition. "If we find that any individual owns more than 51 per cent in two clubs, our rules are very clear. They cannot both compete," he said.
CSKA president Yevgeny Giner is a close friend of Abramovich, the former owner of Sibneft and still the company's major share-holder.
Sibneft, Russia's fifth largest oil company, pledged $18 million a year until 2006 to become CSKA's title sponsor.
UEFA's lawyers will have to work quickly as the competition begins on September 14. Chelsea are due to play CSKA in London on October 20 and in Moscow on November 2.
