Ronaldo is said to want to earn at least as much as Barcelona's Lionel Messi and Paris Saint-Germain ace Neymar.
Links to United could surface as the Portuguese battles to get his way, according to Sky Sports La Liga expert Guillem Balague:
"What is happening is the following. He wants a new contract but not just to equal Messi and Neymar (25m euros net plus) but also because he might have to pay 30m euros to the Spanish tax man.
"A sign on fee would sort that out. Real Madrid have promised him they will give him a new contract and they are talking. So expect a suggestion or two of him going to United as a way to put Real under pressure."
Suggestions of a return to United surfaced this summer after Ronaldo was accused of tax fraud, something he denied, per BBC News. Days after the allegation was made, Kaveh Solhekol of Sky Sports News reported Ronaldo was interested in moving back to Old Trafford.
Ronaldo eventually committed himself to Real but recently hinted he could seek a new deal after helping Los Blancos beat Borussia Dortmund 3-1 in the UEFA Champions League on Tuesday. When asked about the possibility of signing an improved contract, Ronaldo said, per Hamish Mackay of the Daily Mirror: "That's a good question. Perhaps the president would know how to give a better reply than me."
Mackay noted how the prolific Portuguese powerhouse only signed a contract, paying £365,000 per week, in November 2016. Perhaps it's why Los Merengues are resisting the idea of offering fresh terms to Ronaldo, per Jose Felix Diaz of Marca.
Diaz did reveal neither party is unhappy with the situation, contrasting Balague's statement about Real's promise and contract talks with the player. Whatever the reality, the issue of Ronaldo's future never seems to go away for long.
Los Blancos have even taken the step of making it clear their prized asset won't join another heavyweight club on the continent. Real told Spanish outlet Cadena Ser that Ronaldo "will never be transferred to another European club" (h/t Calciomercato.com).
Interestingly, Calciomercato revealed Real "would be willing to deal with non-European companies, with an eye to the...MLS."
Such a scenario would seem more suited to when Ronaldo's deal with Los Blancos runs out in 2021. He will be 36 when that contract expires, so perhaps he would be more willing to consider a move away from top-level European competition.
At the moment, Ronaldo is too valuable for Real to even consider letting him leave. He remains the attacking talisman who has served as the chief inspiration for three Champions League triumphs in the past four seasons.
Zinedine Zidane's team is built around Ronaldo's ruthless efficiency in the final third. Fresh from also winning La Liga last season, only his second since moving to the Spanish capital from United in 2009, Ronaldo may believe the time is ripe to enjoy some sustained domestic dominance.
Keeping Ronaldo happy has to remain Real's top priority. It won't be easy if he is determined to push for a more lucrative contract, though.