The move from the English champions means that they are almost certainly set to miss out on the Brazilian's signature, leaving Barcelona with a clear run to sign him.
Sources in Spain were already suggesting that Barca were close to landing the player and now it seems they are closer than ever.
French reports state that United are belived to have made a new bid of é¼28 million (£19.6 million) on Friday, but this is still short of PSG's valuation.
Barca's bid is still slightly less than United's but they are thought to be offering more add-ons to the fee.
United are now trying to bring the transfer to a conclusion and it looks as if they will be forced to turn their attentions elsewhere.
A statement from the club read: "Negotiations between Manchester United and Paris St Germain and representatives of Ronaldinho have been ongoing for several weeks.
"In order to bring talks to a conclusion the club has spoken again to Paris St Germain and the players' representatives and following our final written offer submitted on Friday morning, we have notified all parties that unless an agreement is reached by 1900CET, Manchester United will withdraw from the process."
The Red Devils are now being strongly tipped to try and hi-jack Chelsea's bid for Blackburn Rovers star Damien Duff.