Gill started every one of Paraguay's five matches at the tournament as the South Americans made an unexpected run to the last 16, eventually bowing out to France.
His displays throughout, including a string of big saves, have caught the eye of recruitment staff well beyond Argentina, with the Manchester Evening News reporting that Manchester United have taken note of the 26-year-old alongside Aston Villa and Ipswich Town, who had already been linked with him. Serie A pair Lazio and Torino have also been credited with interest as his stock continues to rise.
Gill, who has a release clause in the region of £5.2m, addressed the growing speculation directly when asked about his future, striking a measured tone rather than getting carried away by the noise.
"I can't say yes or no. They told me there is interest, but not a formal offer," he said.
"I don't want to get carried away. We'll sit down and speak with the club to see what is best. I have a clause in my contract and I think it has to be respected."
His contract with San Lorenzo runs until 2027, giving the Argentine club no pressure to sell, though his rapidly rising profile means any club moving for him now would likely need to act before his value climbs further. San Lorenzo control half of Gill's economic rights, having bought that stake for a modest fee back in January 2025, a deal that now looks shrewd given his subsequent rise.
Standing at 6ft 6in, Gill has established himself as San Lorenzo's first-choice goalkeeper over the past two seasons and was named player of the match in more than one of Paraguay's World Cup fixtures, underlining the scale of his tournament.
For United specifically, any move would represent competition for Senne Lammens rather than an attempt to unseat him, with the Belgian having enjoyed a strong debut campaign since arriving last summer. Whether interest turns into a concrete offer before the window closes remains to be seen, with United widely expected to prioritise their midfield rebuild over back-up goalkeeping options in the short term.