However, no decision is expected to be made over the new arrival until director Marina Granovskaia returns from a holiday next week. "No further pre-construction design and planning work will occur", a statement issued on the club's official website read.
The expansion of Stamford Bridge to a 60,000-seat capacity was Abramovich's master plan for the west London club.
- Vasco Cotovio contributed reporting.
Abramovich has since relocated to Israel and can now travel to the United Kingdom without a visa.
Could Abramovich walk away from Chelsea?
AMERICA FIRST: Trump SLAMS EU, Canada, Mexico with STEEL Tariffs
It prompted threats of retaliation from the European Union on United States products before the policy was abandoned. Malmstrom is meeting US Trade Representative Robert Lighthizer in Paris today among other global trade chiefs.
But in another article the Times adds that Abramovich would in fact "want £1.17bn back if he sells Chelsea".
Abramovich became Chelsea owner in 2003 and with the help of his financial input, Chelsea were able to appoint Jose Mourinho and win their first two league titles in 50 years.
In a statement, the club did not say whether the decision was related to the visa problems of Abramovich who was reported to have taken Israeli citizenship earlier this week.
Premier league winners in 2016/17, Chelsea missed out on Champions League football by finishing fifth this year, and there is substantial uncertainty around the future of manager Antonio Conte.
Chelsea have been linked with Maurizio Sarri, Luis Enrique and Carlo Ancelotti in recent weeks. It has not been confirmed that the Abramovich situation is the reason, but that is the assumption of most observers.
Chelsea have had talks with former Paris St-Germain coach Laurent Blanc as a possible alternative.