The Sun says United have been quoted £26million but the Red Devils plan to force the price down this weekend.
Old Trafford chiefs will begin the process with a bid of around £11m - but an offer of £15m may be enough to bag the winger.
Robben, 26, is seen as the creative spark which can help fill the void left by £80m Cristiano Ronaldo.
He came close to signing for Alex Ferguson's men from PSV Eindhoven in 2004 when he visited United's training ground.
But he opted for a £12m move to Chelsea.