Gill, 26, was a standout for Paraguay during their 2026 World Cup campaign, putting in a Player of the Match performance in their penalty win over Germany in the round of 32.
His fine performances throughout the tournament have caught the attention of Man United, who are looking for an understudy to Senne Lammens.
Speaking to DSports Radio Gill’s agent Jara has confirmed talks with clubs in England and Germany, including Man United.
"We are in talks with English clubs as well as clubs in Germany. There were enquiries with Manchester United,” he said.
"We only received two concrete offers. We are currently in the negotiation phase.
"The sale is close, the time is right. We have to handle it very carefully because there are many things involved.
“It's ideal for him to take a step up in quality. He's prepared and capable of playing in any league, without a doubt."
He added: "We're trying to finalise it as quickly as possible for everyone's benefit. It would be very important for San Lorenzo; hopefully, it will come to fruition."