Speaking to Sky Sports News, Gill also revealed that even if a deal were to be done that Zaha would not arrive at Old Trafford until the summer, a condition that Palace were determined to be a part of any deal.
“He is one of the players that we are looking at,” said Gill.
"That is all I will say at the moment. I've been in football long enough to say that is not done until it's done. He's one of the players we are looking at, but it is far from done."
Palace have previously claimed that they valued Zaha at £20 million, although the deal is likely to be for less, with significant add-ons included.
If United do complete the signing of Zaha for next season, it is also likely to bring further speculation about current United winger Nani. The Portugal international has less than 18 months remaining on his contract and has been repeatedly linked with a move away from Old Trafford.
In other news, Celtic manager Neil Lennon has revealed that he is trying to tie down reported Manchester Untied target Victor Wanyama to a long-term deal. The Kenyan midfielder has earned rave reviews for his performances, particularly in the Champions League this season, and is thought to be on the radar of United as well as Arsenal.
Despite Wanyama so far rejecting attempts to sign a new deal at Celtic, Lennon has said that he will try again with the 21-year-old and his agent Rob Moore.
“We can always re-open negotiations with Rob on Victor’s situation,” Lennon said, according to the Daily Record.
“He has another two years on his contract so we have time on our side.
“Obviously, the longer we leave it, the more vulnerable we become or the more he is an attractive proposition for a bigger club.
“That scenario will be a reality later on down the line. In the meantime, we will be plugging away at it.
“He has never intimated to me that he wants to leave and I am not too sure who is driving the bus in this situation, whether it is him or Rob.”
Also linked with a move to Manchester United of late is Galatasaray goalkeeper Fernando Muslera. The Uruguayan is one of the names to have come up amid reports that Sir Alex Ferguson is considering replacing current United stopper David de Gea.
Muslera, 26, is said to have impressed Ferguson in during Galatasaray’s meetings with United in this season’s Champions League group phase. And the Uruguayan has said that he would relish a move to England.
“The Premier League is my childhood dream,” he told Turkish publication Haberturk.
“I always want to move forward in football. I started off with Wanderers, then Nacional, then Lazio and then, a step forward, Galatasaray.”
There is nothing new in reports suggesting that Manchester United are interested in Ajax attacking midfielder Christian Eriksen. The 20-year-old has been repeatedly linked to United as well as several of Europe’s biggest clubs for more than two years.
But the Denmark international’s agent has said that Eriksen is still focused on Ajax.
“For the last couple of weeks, and also because of the holidays, the press have kept their distance, which is something [Eriksen] does not regret,” explained Martin Schoots, according to Sky Sports.
"I'm not saying that this means no-one is interested as it would be strange for a player who has been followed by the biggest clubs in football since he was 14 years old to not be on their radar anymore.
"Christian just wants to concentrate on his football, but you never know what might happen in football,” he added intriguingly.