The 21-year-old winger was one of the club's star performers in their recent League Two campaign and manager Peter Jackson confirmed last week that he had offered the former Boston playmaker a new deal that would have made him one of the highest paid players in the club's history.
But N'Guessan has opted to turn down the deal, paving the way for his exit from Sincil Bank.
In a statement on their official website, Lincoln said: "We can confirm that Dany N'Guessan has turned down the offer of a new contract with the club and as such we have granted him permission to talk to other clubs.
"We have, as yet, received no offers for the Frenchman, whose current contract with the club expires on June 30."
N'Guessan has already been linked with moves to Leicester and Sheffield Wednesday and any move could be subject to a tribunal as the player is under 24.