Grant has impressed since leaving Derby County for Stoke City on loan.
Derby County have told Stoke City to pay £4 million if they want to sign Lee Grant permanently in January, the Telegraph reports.
Grant made the surprise switch to Staffordshire on deadline day, but has excelled in the absence of regular goalkeeper Jack Butland.
The 33-year-old is due to return to Derby County early next month, however, and the Rams, who have changed manager since Grant’s departure, appear keen to keep him around.

Grant was a regular during Steve McClaren’s first spell in charge, but fell out of favour under Paul Clement and later Nigel Pearson.
However, with Derby number one Scott Carson impressing in recent weeks and Grant’s contract set to expire in June, the Rams’ alleged asking price does seem a little steep.
Perhaps unsurprisingly, Stoke boss Mark Hughes has admitted he is weighing up alternatives to the former England Under-21 international.
“We would like to get something done, but they [Derby County] are asking for too much money at the moment,” the Welshman said, as quoted by the Telegraph.

“We have a fee we feel he is worth – a market value, and because he has been doing well we expect there to be a premium, but we aren’t going to be held to ransom.
“If it doesn’t change soon then we will have to look at other options.”
Hughes is said to have targeted Ingolstadt keeper Ørjan Nyland should he fail to prise Grant away from Pride Park.
The 26-year-old has a market value of £850,000, according to Transfermarkt.
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