The international star has played little part on the pitch since joining from Bolton Wanderers in 2008 and was even loaned out to Barnsley last season.
The new Premier League campaign hasn’t offered the ex-Zob Ahan man any cause for optimism.
"Unfortunately, I had couple of injuries recently. I will resume training after ten days, but it remains to be seen when I will be fit to play,” Teymourian said according to Persianfootball.com.
"I am not very pleased with my current situation. It seems that no matter how I train. It won't make any difference to my coach.
"In this situation, I care more about playing football than financial matters. I have discussed it with Roy Hodgson, but no convincing explanation has been given."
The Team Melli man is now thinking about pastures new as he attempts to rebuild his European career.
"Unfortunately, I haven't been given any opportunities. In these circumstances, I might consider leaving Fulham", he added.
"I had a few offers, but none of them were considerable. I have now to wait and see what happens in the coming days.”