The paper also reports that the Swans are waiting to hear back on thei bid which is rumoured to be betwen £2 million and £3 million.
And the paper also says that Stockdale is keen on a move to South Wales to become Swansea's Number 1 after previous incumbent Dorus De Vries left for Wolves.
The Post reports: But Swansea remain hopeful that they can convince the Cottagers to do business — even though Championship side Leeds, Stockdale's home city club, have declared an interest in taking him on loan.
Rodgers has identified Stockdale as his top goalkeeping target after Dorus de Vries quit the Liberty to sign for Wolves.
He believes the England squad member will thrive as Swansea's No. 1, and it is thought Stockdale is keen on a move to Wales.
But persuading Fulham to say a permanent goodbye to a keeper who is rated highly may take some doing.
New Craven Cottage boss Martin Jol has made it clear that veteran Australian international Mark Schwarzer will be his first choice in goal next season.
But he has also stressed that Stockdale is highly regarded and has said there are no plans to sell.
"I am actually quite calm about the situation," said Rodgers.
"The important thing is to get the right keeper in, not just to go and get someone.
"We are taking our time and we haven't jumped into anything.
"What is important is that we get a keeper who fits us right.
"There are plenty of keepers out there, but there are not many who will suit the way we do things."
This article first appeared on JACKARMY.net.