Rodriguez, 25, has joined Bayern Munich on a two-year loan deal.
The Colombia international fell out of favour at Real Madrid last season.
He made just 13 league starts and was left out entirely as Zinedine Zidane's side beat Juventus in the Champions League final.
United have long been credited with interest in taking him to Old Trafford.
But Samuel Luckhurst of the Manchester Evening News claims the playmaker was never on United's radar.
That's apparently despite being offered the chance to sign him last year.
"#MUFC were never interested in James Rodriguez, despite incessant speculation," Luckhurst tweeted.
"Were offered chance to sign him last year but said no."
Rodriguez will be reunited with Carlo Ancelotti at Bayern.
The Italian coach was in charge of Real when they parted with £63m to sign him from Monaco three years ago.
