Krishna had given many offers to Karna to fight against Kauravas by joining Pandavas. Here is the the summary of that conversations between the Krishna and Karna before Kurukshetra battle.
It’s a fascinating conversation between Karna and Krishna. As the Kurukhetra war becomes imminent, Krishna grew restless on the fact that there are excellent warriors in Kaurava camp. Attempts were to be made to bring some of them to the Pandava’s side. He did a detailed analysis of all the excellent warriors. For example:
Bheesma: The oldest and the mightiest force was Bheesma. Bheesma however had committed a sin of kidnapping three maiden daughters of Kashi king– Amba, Ambika, Ambalika. One of the princesses was reborn in the form of Shikhandi. Krishna knew the truth of the re-incarnation of Amba, who had pledged to become the reason of Bhessma’s death.