The Blues are currently one of three Premier League clubs yet to make a new signing during the summer transfer window, but there are signs that new owner Todd Boehly is proactively looking to change that.
However, at a time when the English giants have their own strategy in place, developments elsewhere have led to speculation regarding two high-profile additions.
According to the Evening Standard, Chelsea have been asked whether they are prepared to enter the race for each of the two attackers.
As far as Ronaldo is concerned, United have insisted on more than one occasion that the Portuguese superstar is not for sale and will remain at Old Trafford for 2022-23.
Nevertheless, it was revealed late last month that agent Jorge Mendes had held discussions with Boehly in order to determine the level of interest from Chelsea's side.
Ronaldo, who is technically tied to United until 2024 due to his club possessing a 12-month option on his contract, netted 24 goals during his first season back in the Premier League.
Neymar still has five years remaining on his deal with PSG, a two-year extension automatically being activated as recently as June 30.
Chelsea are one of a handful of clubs who may give consideration to signing Neymar given the Brazil international's wages at Parc des Princes and his team allegedly wanting to receive in the region of £190m.
Juventus have been linked with Neymar, although it is unclear whether the Serie A outfit will want to match any offer which comes from Chelsea. body check tags ::