Pogba's future at Old Trafford has been the subject of speculation this season following reports that he has fallen out with manager Jose Mourinho, and he lost his place in the United starting XI at one point during the campaign.
Both United and Madrid are expected to undergo major overhauls of their squads this summer after finishing a long way behind Manchester City and Barcelona respectively, with Ronaldo one of the high-profile players linked with an exit from the Bernabeu.
Diario Gol reports that the 33-year-old is Mourinho's top transfer target this summer, and that he is willing to offer Pogba plus an extra £70m to land the prolific Portugal international.
Ronaldo played for United from 2003 to 2009, scoring 118 goals in 292 appearances for the club.
The five-time Ballon d'Or winner has since netted 450 times in just 437 games for Madrid, and could win his fifth Champions League title against Liverpool this evening.