The Toffees have had a perfect start to their Premier League campaign, winning each of their four games so far and sitting atop the table.
However, England international Jordan Pickford’s shakiness in goal and vulnerability has caused concerns for Carlo Ancelotti.
He was at fault for the goal Neal Maupay scored in Everton’s 4-2 win against Brighton and Ancelotti is now looking to bring in a new goalkeeper to challenge Pickford.
Everton have contacted league rivals Manchester United over a deal for Romero and Tottenham over a deal for Gazzaniga, with little time remaining in the transfer window.
However, the Toffees prefer to sign one of Romero or Gazzaniga on a loan deal while Manchester United and Tottenham want permanent exits for their goalkeepers.
With just hours remaining in the window before it slams shut, it remains to be seen if Everton can reach an agreement with their league rivals over a new goalkeeper.
Both Manchester United and Tottenham have back-up goalkeepers in the shape of Dean Henderson and Joe Hart, respectively, and would be willing to let go of Romero and Gazzaniga if a respectable bid comes in.