Rooney, who joined United from Everton in 2004 in a £25.6m deal, wants to leave Old Trafford because he claims the club cannot match his ambition.
The 24-year-old England international has concerns over the squad's strength and said Gill had not given him "any of the assurances I was seeking about the future squad".
Ferguson, who revealed in a news conference on Tuesday that Rooney was not intending to extend his contract beyond the summer of 2012, said he wanted a quick resolution to the matter.
After the Champions League victory over Bursaspor on Wednesday, the Scot said: "We don't want it to become a saga. What is really important is for us to put it to bed."
But Thursday's statement from the club suggested the situation might take a while to resolve.
"We are aware that there is intense public and media interest on the club at the moment but there are no developments of note to report," it read.
"We can confirm a number of meetings have taken place today, including with the player's representative.
"The outcome of those meetings will become clear in the near future. In the meantime, fans are asked to be patient."
Sometimes you look in a field and see a cow. You think it is a better cow than the one you see in your field. It never really works out that way
Sir Alex Ferguson
Rooney's decision to leave Old Trafford has rocked Manchester United, with Ferguson himself admitting he was "shocked", "disappointed" and "bemused" by the development.
Some United supporters have expressed concerns about the club's future given the amount of debt placed on the club by US-based owners the Glazer family following their leveraged buyout in 2005.
Two weeks ago, United reported an annual pre-tax loss of £79.6m for the 12 months to 30 June after recording a profit of £48m for the year before.
However, Ferguson believes the club remains in good shape.
"We will be OK. I have every confidence," said the Scot.
"The structure of the club is good. We have the right staff, the right manager, a brilliant chief executive. There is not a thing wrong with Manchester United.
"To maintain the success at any club is not a certainty. I always believe a four-year cycle is the most you can achieve. Very few teams can go beyond that.
"We realised some time ago that Ryan Giggs, Paul Scholes and Gary Neville were not going to last forever. Therefore our policy is to develop footballers in their place."
Holloway's rage against Rooney saga
Ferguson added: "That is the problem with potential. People don't identify [it]. We are very good at it. I have identified it all my life. I know potential. I know where it can be developed and how to develop it. I have faith in it.
"That is what this club is about. When you see Manchester United at the moment, with 14 players under 22, you don't see the Manchester United for years ahead."
Former Manchester United captain Roy Keane, now manager at Ipswich, said the Old Trafford club would cope without Rooney.
"Players have opinions and if they want to leave then good luck to them," he said. "Man Utd will more than survive."
Asked if Ferguson's side could still attract top quality players, the Irishman added: "Absolutely, of course, absolutely."
Rooney is currently sidelined because of an ankle injury picked up in training ahead of the game against Bursaspor.
However, Ferguson dismissed suggestions he might suspend his striker when he returns to fitness.
He also expressed doubts as to whether Rooney could find a better employer.
"Sometimes you look in a field and see a cow," said Ferguson. "You think it is a better cow than the one you see in your field. It never really works out that way.
"Some players like to think the world is better somewhere else. It never really works."
Manchester City and Chelsea have been linked with a move for Rooney but City boss Roberto Mancini has played down talk of a move for United's prize asset.
"It was different for Carlos Tevez [who moved between the clubs last summer]," said the Italian.
"Rooney is English and has played for United for a long time, Carlos was there for two years. That makes a difference."
Rooney's club-mates are determined to retain their focus while they wait for the striker's future to be resolved.
"You have to accept big players and big stars move on at every club," said midfielder Darren Fletcher.
"We should all remember what a big club Manchester United is. The biggest in the world. High-profile players have left in the past but the club itself just keeps going.
"If anything, it should galvanise the squad because we all need to come together. The fans need to trust us and get behind the team."
Left-back Patrice Evra hopes Rooney remains at Old Trafford.
"Wayne is one of the best players we have. Everyone knows that," said the France international.
"I don't really know what he has said but I hope he gets fit quickly and I sincerely hope he plays for us again. But I am not Wayne Rooney. I am not Sir Alex Ferguson."
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