Real Madrid have made an improved £10.3m bid for unsettled Manchester United striker Ruud van Nistelrooy.
Bayern Munich were favourites to sign the 30-year-old, who handed in a written transfer request after a row with United boss Sir Alex Ferguson.
But Real have upped the stakes and a spokesman said on Wednesday: "The club have made a new offer and are waiting for a reply from Manchester."
Van Nistelrooy returned to training on Monday, despite his uncertain future.
It now remains to be seen whether Bayern respond after claiming they were on the verge of closing a deal, and that Van Nistelrooy himself was keen to move to Germany.
Bayern president Franz Beckenbauer was confident a deal will be struck for Van Nistelrooy, adding that they will offload Roy Makaay or Claudio Pizarro.
"We're still Euros 5m (£3.4m) away from Manchester United's valuation, but the chances are still high," he said.
"But if it does work out, I could imagine us giving away Roy Makaay or Claudio Pizarro."
Bayern have already spent £7.15m on Germany international Lukas Podolski from Cologne.
I couldn't tell you why he wants to leave or why his heart isn't in it
And with Makaay, Pizarro and Paraguay's Roque Santa Cruz already on the club's books, Van Nistelrooy's arrival "would leave us with too many strikers", according to Beckenbauer.
Paolo Guerrero was sold to Hamburg and Beckenbauer claims further departures to the north may be on the cards as their Bundesliga rivals are in the market for a striker, having failed to land Milan Baros or Patrick Kluivert.
"We could reach another deal with Hamburg," he added.
United boss Ferguson revealed that Van Nistelrooy has asked to leave Old Trafford three times since May 2005.
"Ruud asked away before the Arsenal FA Cup final last year, then asked away through his representative, and has now asked away himself in writing," he told the News of the World.
"Quite frankly, if he wants to leave, there really is no point trying to persuade him to stay.
"I couldn't tell you why he wants to leave or why his heart isn't in it - all I can tell you is that he has asked away and we have accepted that."
Bayern are openly admitting they have held talks with the player.
"He wants to come to us. Now the ball's in Manchester United's court," Bayern general manager Uli Hoeness told the Bundesliga club's website on Sunday.
And Bayern club president Karl-Heinz Rummenigge told the Bild newspaper: "Ruud has told us he would like to play for us next season. We have already spoken about money with him but it would be United who will finally decide."
United signed Van Nistelrooy for £19m from PSV Eindhoven in 2001.