The Sunday Mirror/i> says Cottagers boss Mark Hughes sees Australian international Federici as the ideal replacement for the unsettled Mark Schwarzer, who is still being linked with a move to Arsenal.
Federici, 24, is out of contract with Reading at the end of the season and is yet to agree a new deal.
Royals boss Brian McDermott said: "We've had no offer for Feds but with the deadline coming up, who knows what will happen?
"The fact is a number of players have left this club. If things happen after the weekend we'll have to look closely at it."