A talkSPORT report claims the 21-year-old playmaker has emerged as a January target for the Italian champions, who are ready to strike first to beat United to his signature.
Rodriguez has been tipped as the 'new Cristiano Ronaldo' in several reports, and the Old Trafford club have watched him on numerous occasions this season.
The Porto attacking midfielder has been in excellent form for his Portuguese club, helping them to qualify for the last-16 of the Champions League.
Rodriguez has been linked with a summer move to Manchester United, and talkSPORT claim he could be signed as a direct replacement for Portuguese winger Nani if the former-Sporting star leaves the club at the end of the season.
But Portuguese newspaper A Bola has suggested that Juventus are prepared to make the first move for Rodriguez, although they claim the bidding war could ultimately come down to which club is able to meet the Porto star's £38m minimum fee release clause.
The Colombian international has stepped up his performances this season, and is rated as one of the best young players in Europe.
His link-up play with Porto teammate Jackson Martinez is one of the main reasons for the club's impressive European performances, and his displays could earn him a move to one of Europe's top leagues before long.