Despite having spent in excess of £1bn across three transfer windows, it has been widely claimed that Todd Boehly and Clearlake Capital are prepared to conduct further business.
Head coach Mauricio Pochettino allegedly feels that his squad could benefit from a new central defender, central midfielder and forward to boost their chances of a return to Europe.
Furthermore, the Argentine is said to want more height at his disposal, yet Chelsea may have to part ways with a number of players before deals can go through.
Although Conor Gallagher is expected to stay at Stamford Bridge, Borussia Dortmund are in talks to sign Ian Maatsen and Trevoh Chalobah is known to be available for transfer.
According to The Sun, the West Londoners hold an interest in securing the services of Paredes before the end of the month.
The 23-year-old has played a key role for Athletic this campaign, making a total of 17 appearances and two substitute outings in La Liga.
Athletic currently possess the third-best defensive record in Spain's top flight and sit in fourth position, ahead of Atletico Madrid on goal difference.
Given those circumstances, Athletic are unlikely to be open to cashing in on Paredes unless they receive an offer in January that is too lucrative to refuse.
Nevertheless, the report claims that Chelsea have sent a scout to assess the progress of Paredes on seven occasions this campaign, an indication of their admiration.
Paredes is also a former Spain Under-21 international whose performances have put him in contention to represent his country at Euro 2024, despite currently being uncapped for the seniors.
On a negative note for Chelsea, Athletic have reportedly refused to name an asking price for Paredes, but he does have just 18 months remaining on his contract.
Chelsea have lacked clean sheets during their first season under Pochettino, keeping just seven shutouts in 25 matches in all competitions.