Dempsey struck his second consecutive hat-trick on the weekend.
Redknapp wrote in the Daily Mail: "Clint Dempsey is in the middle of the best form of his career. Another hat-trick on Saturday as Fulham overpowered a disappointing Newcastle takes his tally for the season to 15 goals in all competitions. He is versatile, being able to play in numerous positions.
"He is only 28. I wonder if a bigger club would take a gamble on his goals and if Fulham would sell?"