The 29-year-old joined Reading on a free transfer from Stuttgart last summer after impressing during a loan spell with Fulham.
However, the Russia international could only manage five goals in the Premier League as the Royals suffered relegation straight back to the Championship.
Pogrebnyak is now almost certain to leave the Madejski Stadium this summer, with Reading owner Anton Zingarevich confirming in May that the player had a relegation release clause in his contract.
His agent, Oleg Artemov, says he has received offers from Premier League clubs and Pogrebnyak is keen to stay in the division.
However, the striker has also refused to rule out a return to Russia, where he has previously enjoyed spells with the likes of Spartak Moscow and Zenit St Petersburg.
"It's true that my dream is to continue my career in England, in the Premier League. But I wouldn't deny a move to Russia," he told sovsport.ru.
"On the contrary, the best moments of my career are from the Russian championship. So anything can happen."