A source with knowledge of the situation told Press Association Sport that two Chelsea supporters were believed to have been stabbed on Tuesday evening, although it was understood neither required any hospital treatment.
Earlier in the evening, a spokeswoman for the Chelsea Supporters' Group expressed surprise at the suggestion of problems facing visiting fans, saying the atmosphere in the city was peaceful.
English fans have been victims of violence in Istanbul before, with Leeds fans Christopher Loftus and Kevin Speight stabbed to death before a UEFA Cup tie in 2000.
The Foreign Office later confirmed it was investigating reports of the incidents which took place around Taksim Square.
"We are looking into reports," said a Foreign Office spokeswoman.
"We have had no confirmation of an incident. If confirmed we stand ready to provide consular assistance."