It is unclear which terms Hannibal was seeking exactly. Polybius' account of what happened after Cannae is lost to us and Livy only mentions that Hannibal's ambassador Carthalo was to propose terms, without mentioning which. Carthalo was sent to Rome with ten captured Romans, who were to propose a ransom for all the captured soldiers to the Senate. The ransom could be conducted independently of any peace talks, but the Romans refused both.
What terms would Hannibal have been seeking? Hannibal had crushed Roman armies on three occasions in just two years - the third army being the largest Roman army ever raised - so he probably felt that he could dictate terms. As was usual in this era, an indemnity in gold or silver would have been part of the terms, to be paid over the course of several years (or even decades). There would be additional demands though.
The Second Punic War had started over Saguntum, a city friendly to Rome, located on the coast of Spain well south of the Ebro river. Hannibal alleged the Romans had broken a treaty which had divided the Iberian peninsula in a Carthaginian sphere of influence (south of the Ebro river) and a Roman sphere of influence (north of the Ebro river). Part of Hannibal's peace terms would be either renewal of the Ebro treaty, or a similar treaty with another dividing line (the Pyrenees perhaps).
Furthermore, Hannibal was motivated by revenge for the humiliating defeat the Romans had brought Carthage in the First Punic War. If Hannibal felt his victories were decisive enough, he probably would have demanded control over Sicily and Sardinia, islands which were once under Carthaginian control but were lost to the Romans in the wake of the First Punic War.
Lastly and probably least of all, Hannibal may have demanded independence for Italian cities, to reduce Rome's influence on the peninsula. If we can speak of an overarching strategic goal for Hannibal, it was not to destroy Rome* but to reduce Rome's status to that of a minor regional power - basically the situation before the First Punic War. Carthage for over a century had been a large, and for while even the dominant, power in the western Mediterranean. In the First Punic War Rome had challenged that power, resulting in Rome becoming the main rival of Carthage for dominance in the western Mediterranean. Hannibal wanted to put an end to that by putting Rome back in it's place as a comparatively small local power.
*Hannibal was not out to destroy Rome. Warfare in the Hellenistic tradition (which both Carthage and Rome could be considered part of, certainly initially) often was about influence and control, not so much about completely destroying enemies. If an enemy was defeated and sued for peace, terms were imposed and the war was over. Rome was unique in that regard; Romans did not consider a war over until they had won, period. Conceding was not an option for the Romans, as other Hellenistic rulers had discovered (Pyrrhus for example).