Ronaldo is a free agent after agreeing to cancel his contract at United in the wake of his explosive interview in which he criticised the club.
Chelsea considered a move to sign Ronaldo in the summer after the 37-year-old was offered to Blues co-owner Todd Boehly by his agent Jorge Mendes.
Boehly discussed the prospect of signing Ronaldo with Thomas Tuchel but then Chelsea head coach knocked back the idea.
Ronaldo is now searching for a new club in January after he waived the £15.5million he was owed on his United contract, which had been due to expire next summer, to force through his Old Trafford exit.
But Chelsea are aware the Portugal international will not fit new manager Graham Potter’s style of play and currently have no plans to move for him.
The Blues have moved to sign RB Leipzig forward Christopher Nkunku and are confident of sealing a £50m move for the 25-year-old next summer.
Parties on all sides of the deal for Nkunku are tight-lipped on whether the deal has been completed, but several sources around Chelsea believe it is done.
The signing of further forwards is reliant on player sales, with Hakim Ziyech wanted by AC Milan and Christian Pulisic attracting interest from Juventus.