The 21-year old Colombian has been United's radar since last season but have taken a step back after Porto increased the players valuation from £24m to £36m.
However, United can still come up with a deal with Nani and Anderson ready to make way at the end of the season for a part-exchange deal, accordding to reports in the Daily Mail.
Anderson, who was bought for around £20m in 2007, has been fighting for a first-team place with Tom Cleverley, Ryan Giggs and Michael Carrick. The Brazilian midfielder, who admitted a return to the Estadio do Dragao could be possible, has failed to perform at the standard United expected him to.
Nani, on the other hand, has been struggling with injuries and did not agree to sign a contract deal with the Red Devils, threatning to buy out his contract which ends in 2014.
The Portuguese has been linked with a move to Zenit St Petersburg, Juventus and even Arsenal but is slowly finsding his feet back into the starting XI. Nani faces competition from a host wingers like Antonio Valencia, Ashley Young, Ryan Giggs and Shinji Kagawa.
United are likely to get rid of either Nani or Anderson to make way for Rodriguez. Sir Alex Ferguson also signed Crystal Palace's Wilfried Zaha, who will join them at the end of the season.
United are also interested in Benfica pair Nicolas Gaitan and Ezequiel Garay. The Red Devils will battle with Liverpool for 24-year old Dede from Brazilian Vasco da Gama.