The Daily Mail says United boss Sir Alex Ferguson has been on the trail of Rodriguez for months and despatched a scout to watch him in Porto's latest Portuguese League game against Maritimo at the Estadio do Dragao on Friday night.
But United have been shocked by news that Rodriguez has renegotiated his Porto deal and agreed a significant increase in his transfer market valuation.
When United last enquired about cost, they were told they would have to pay £24million to buy him out of his contract. However, now the release clause stands at £36million.
United have a ready-made bargaining tool in unsettled Portugal winger Nani, who could be used in a part-exchange package.