The South Korean’s current deal is set to expire at the end of the season but United boss Sir Alex Ferguson is keen on keeping him at the club.
“We have had discussions with him and told him we are going to do it,” said Gill.
“It won’t be done before the start of the season, but it will be pretty soon afterwards.”
Park joined United from Dutch giants PSV Eindhoven in 2005.
Ferguson said: “When we were scouting him at PSV, I saw him in two Champions League quarter-finals and we identified a player with great understanding of space.
“His movement was always very clever – especially in attacking areas – and we felt we needed somebody who could penetrate in the final areas.
“Since then, he has developed his technical and tactical ability. He has done very well and become an important player for us.”
