Imps manager Peter Jackson has offered the French winger three new deals that would have made him one of the highest paid players in the club's history, but the 21-year-old has opted to reject them all.
As a result, Lincoln announced on Wednesday that N'Guessan would be leaving the club this summer and Roberts believes he will now sign for for Walkers Stadium outfit.
"We made Dany a third good offer to keep him at the club," Roberts told the Lincolnshire Echo.
"We made the best offer we could, but Dany has rejected that offer and we have given him permission to talk to other clubs. He is in talks with Leicester, who seem pretty confident about signing him. If he agrees terms, it will be down to the two clubs to agree a
Should the two clubs fail to agree a price for N'Guessan, the fee will be decided by a tribunal as he is under 24.