Chelsea are in “borrowed time” for the sale of the club, says culture secretary Nadine Dorries.
“There is a very short window left for this sale to take place,” Dorries said.
The Blues operate under a special UK government license which ends on May 31.
The license was issued in March when Abramovich was sanctioned.
“Chelsea are sold, as you know, and the penalties apply, so those penalties still apply during the sale,” Dorries told the BBC Newscast podcast.
“But what I will say, actually, is that Chelsea are on borrowed time at the moment.”
When asked how soon the club should be sold, Dorries replied “[within] weeks”.
There is currently three candidates vying to buy Chelsea for around £2 billion.
They are consortia led by Sir Martin Broughton, Los Angeles Dodgers co-owner Todd Boehly and Boston Celtics co-owner Stephen Pagliuca.
US bank Raine Group has been tasked with selling Chelsea and the UK government is expected to issue a new license, allowing the club to be sold once a preferred buyer has been identified.
There were reports on Thursday that bidders were asked to offer an additional £500m to the club.
Any sale can only be signed by the bidder who passes the Premier League owners and directors test.