The France international has long been linked with a move to the Premier League, with Manchester United and Tottenham Hotspur said to be keen.
Everton, Sunderland, Inter Milan, Juventus and Napoli are also reported to be closely monitoring Cissokho’s situation in France.
Lyon have already conceded that they will look to move players on this summer in an effort to generate much-needed transfer funds.
Cissokho is among their most saleable assets and would be happy to take on a new challenge if the opportunity arises.
“The preference would be to depart,” the 24-year-old’s brother and agent Mamadou Cissokho told France Football.
“Aly wishes to discover a new challenge. If he has to stay he will and will do his job, but if there is an opportunity he will seize it.
“The priority is England or Italy. However, there have been no concrete offers as yet, even though Lyon are keen to sell.”
While the Ligue 1 outfit are open to offers, their asking price for Cissokho is considered to be too high – especially as club president Jean-Michel Aulas recently criticised the defender, among others, in public.
“Aulas made a show in the press and now he has to take his words into consideration and be sensible about a fee,” added Mamadou Cissokho.
“If he doesn’t want the player, he has to let him leave for the right price. €11million for a full-back is impossible nowadays.”