The Russian international enjoyed a successful five months with the West London side, netting six goals in 12 appearances.
Pogrebnyak is now a free agent after failing to agree a new deal with VfB Stuttgart, which has seen the Cottagers emerge as front-runners to sign him permanently.
However, Martin Jol faces competition from Aston Villa and Reading, who are also keen on the 28-year-old.
"After three or four months, I feel that I have found my place in England and I want to play in this league," Pogrebnyak told Sport-Express.
"I feel great desire and strength inside me and my age will not work against me.
"We couldn't agree anything with Fulham so far, but I hope everything will be alright.
"If I don't play for Fulham, I hope to find another team.
"It would be good to sort this out before the European Championship, because there is a risk there. Anything could happen, and if you get injured then no-one will want to sign you."
