"By Wednesday we should have a definitive verdict on whether Ronaldinho goes to Manchester or if he stays," Assis said.
Assis indicated that the World Cup-winning star had no problems with the terms offered by United who look to have seen off competition from Real Madrid and Barcelona, providing PSG agree to release their prized asset who is contracted to the Parc des Princes club until 2006.
"The most difficult thing is for the clubs (PSG and United) to reach an agreement," said Assis.
"We have no problems."
Asked about how Ronaldinho viewed a move to Old Trafford, Assis said: "He is calm. Whatever happens he has a good contract with PSG. He is currently in Brazil on holiday but he is eager to see what is going to happen regarding his transfer.
"Negotiations are still ongoing between clubs but things are going as well as we had hoped for."
PSG's new coach Vahid Halilhodzic had indicated, on replacing Luis Fernandez at the end of the season, that he would not allow the Brazilian to depart.
Halilhodzic, together with his friend and incoming president, Francis Graille, had said they would do everything in their power to keep the 23-year-old on board despite a chequered career under Fernandez whose relationship with the Brazilian had broken down.
However, French football's financial watchdog, the DNCG, has told the capital club they will not be allowed to recruit any players until they have balanced their books and now Ronaldinho's sale may be the only way the club can unblock the situation.
Halilhodzic admitted as much last week when he said: "At the start I did not think the situation was that bad.
"That is why I said that Ronnie would stay. But if a club makes a big offer we will not be able to keep him. If a player does not want to play, you cannot do anything."
A frenzied week of transfer activity for Manchester United is set to start with the arrival of David Bellion.
The 20-year-old's Sunderland contract expires today and confirmation of his long-anticipated move to United should come within the next 24 hours as Alex Ferguson's starts his summer rebuilding programme.
It is the first in a series of moves to be concluded over the next few days, with Nantes £3.5million-rated Cameroon midfielder Eric Djemba Djemba also on Ferguson's hit-list.
In addition, David Beckham's £25million departure will be confirmed at a frenzied media gathering tomorrow providing he passes his Real Madrid medical today.
Bellion has long been pursued by Ferguson, who tried twice to land the Paris-born player during the January transfer window, only to meet with a stinging rebuff from Sunderland owner Bob Murray, who accused United of trying to land the pacy winger 'on the cheap'.
The arrival of Djemba Djemba though is seen as a useful addition to Ferguson's squad.
The 22-year-old was part of the Cameroon side which put aside the tragedy of Marc-Vivien Foe's untimely death to play in the Confederations Cup final defeat against France.
"To play for Manchester United would be amazing for me," said Djemba Djemba. "I am young and I have potential and I want to prove to them that I can do it."
Meanwhile, Inter Milan directors admit they are monitoring the form of United winger Ryan Giggs and Arsenal's Fredrik Ljungberg but say no formal bid has yet been lodged for either player.
Inter have long been reported to be monitoring Giggs with yesterday's Italian press claiming that president Massimo Moratti would fly to Manchester this week to talk to United chiefs.
Meanwhile, Arsenal pair Ljungberg and Robert Pires have also been linked with the San Siro club although interest in Frenchman Pires seems to have cooled since the signing by Inter of Sabri Lamouchi.
The club's director general, Massimo Moretti, not to be confused with Moratti said Giggs would fit the profile of Inter.
"We are interested in wingers because there are very few of the them available," Moretti said.
"We are not in a hurry to make a signing. We have time and we are evaluating our options and what is available in the market."
Barcelona will make Turkish keeper Rustu Recber, the first new signing of the Laporta era today, subject to him passing the second half of his medical.