The Colombian has been in impressive form for the Portuguese club, scoring eight goals and managing one assist in 20 appearances in all competitions this season.
The report claims United sent their scouts to watch the 21-year-old in action during Porto's game against Rio Ave last weekend. Rodriguez, who is widely heralded as the new Cristiano Ronaldo, has been monitored by Sir Alex Ferguson and his scouts throughout this season.
The former Banfield star has been strongly linked with a move to Old Trafford in recent times as the Metro earlier reported United are looking to sell Luis Nani to raise funds to sign Rodriguez in the summer.
The Portuguese will have a year left on his current deal in the summer and the Sun claims Ferguson will offer £90,000 a week to keep him at the club. However, it is unlikely that Nani could agree to such a deal as the winger is looking for a weekly wage of £130,000 to continue his services at Old Trafford.
Should the former Sporting player fail to sign a contract extension before this summer, United will be looking to sell the Portuguese international at the end of the season, rather than letting him leave for free a year later.
The Premier League leaders have already found a replacement with the signing of Wilfried Zaha from Crystal Palace, who will join the club next season.
Fabio: I Wanted to Celebrate Rafael's Goal
Meanwhile United full-back Fabio claimed he wanted to celebrate his twin brother Rafael's stunning goal against at QPR - even though he is currently on loan at the West London club.
"I was pleased to see my brother score a goal like that. Naturally I wanted to celebrate, but I was sitting next to the QPR president!" Fabio admitted.
Despite his divided loyalties last Saturday, Fabio believes his loan spell with the west London club has helped him to develop as a player, while his brother has thrived at United.
"I've grown a lot this season. We've both matured, [Rafael is] is flying and I'm playing more. The change has been good for us," he said.
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