The Monaco winger has been one of the tournament’s standout performers so far, netting three goals in as many victories to send his nation through to the last 16 as winners of Group C.
With recent rumours in France having indicated that he was willing to consider a move away from the Ligue 1 runners-up after just 12 months at the Stade Louis II, talk of a switch has intensified.
Tottenham and United are two names in the mix according to reports, and their interest could intensify when the competition draws to a close next month.
One problem could be Rodriguez’s valuation, which is likely to have increased beyond the £35m Monaco paid Porto, due to his exploits in Brazil.
United were linked with the 22-year-old before he switched to the Mediterranean coast, and it is understood that Louis van Gaal has the funds in place to make one or two massive purchases.
Spurs are unlikely to be open to splashing such a sum following Andre Villas-Boas’ much-criticised £110m shopping spree last summer.