New reports out of South America suggest the Premier League club remain firmly in contention for his signature.
Gill has been among the standout performers of the tournament, earning recognition as the highest-rated San Lorenzo goalkeeper of the group stage in FIFA's official Power Rankings.
His stock rose further still when he saved two penalties against Germany, a shootout victory that sent Paraguay through to the last 16.
According to Paraguayan outlet Doble Amarilla, Ipswich are among a group of European clubs monitoring the 26-year-old, alongside Torino, who are also in the market for a new goalkeeper.
The Serie A side have reportedly valued Gill at between €5m and €6m (£4.3m–£5.2m), though Ipswich's interest in the player predates Torino's involvement.
This is not a new story for Ipswich: the club were strongly linked with Gill during last year's transfer window too, with reports at the time suggesting they were ready to offer around €6m (£5.2m).
That deal never materialised, but his World Cup form has now put him firmly back on the club's radar, with a change of representation adding fresh momentum to the story.
Journalist Andres Rolon reported in June that Gill had switched agents and is now with Creer Group, the agency run by former Argentina international Javier Saviola, with expectations already growing that a European transfer would become increasingly likely once the World Cup concluded.
Ipswich are also pursuing business elsewhere, having lodged a rival bid for Toulouse striker Emersonn, a player also being tracked by fellow-promoted side Hull City.
The 21-year-old Brazilian, full name Emersonn Correia da Silva, joined Toulouse in September 2025 after a difficult spell in Turkey with Goztepe, and made an immediate impact in Ligue 1, scoring seven goals and providing three assists across all competitions last season.
Hull had tabled a new offer worth £22.3m for the forward, but Ipswich's rival move means the Tigers' pursuit is no longer straightforward, with the Brazilian's rapid rise in value since his initial €3.2m transfer from Goztepe attracting wider European interest.