It's a very interesting question with a slightly complicated answer, but i will try to give it a go.

For the most of the 15th century the main power in South India was the Hindi Vijayanagara empire, which at its peak definitely had undisputed possession over Malabar coast and Calicut and it's ruler Zamorin. The exact form of this "possession" is unclear, but it seems most likely it was exercised as recognition of overlordship followed by tribute payments by Calicut, while the Vijayanagara left them to control themselves in most matters.

The main rival of the Vijayanagara at the time was the Muslim Bahmani Sultanate situated in the Deccan plateau (founded after rebelling from the Delhi Sultanate in the 14th century). The two states frequently clashed. In the last few decades of the 15th century both of these rivals went through major difficulties. In 1490s Bahmani sultanate started disintegrating into what are known as Deccan sultanates.
At the same time Vijayanagara was experiencing series of dynastic overthrows, rebellions, as well as continuiton of the struggle with the Bahmani / Deccan sultanates.

In this period the relationship of Calicut and Malabar coast with their overlords is slightly unclear. They would nominally still be vassals of Vijayanagara, but it is possible that the Zamorin used the opportunity while the Vijayanagara was distracted and renegaded completely from his obligations, protected from the rest of the Vijayanagara territory by the Western Ghant mountains. But it is, I think, more probable the Zamorin continued with the tribute, while retaining his semi-independant status.

In any case, the arriving Portuguese considered Calicut fully independent entity / kingdom. For example Tome Pires in his Suma Oriental written in 1510s marks that Malabar is bordering kingdom of "Narsinga" (how he calls the Vijayanagara empire) It is possible he is just uninformed about the internal dynamics between the two though and unaware of the client state status. Earlier in his text he considered the Deccan sultanates as one sultanate (Bahmani), while the process of dissolution was already on the way (he does recognize that there are several power holders in the kingdom, which probably are the independent sultanates). It could be just the reflection of the uncertainty of the situation but it does make Portuguese unreliable sources for the political relationships of the Indian subcontinent. However Fernao Nunes, in his embassy to Vijayanagara court in 1530s, mentions specifically King of Caleco (Calicut) as a vassal of Kings of Vijayanagara. This is much later though, and might not apply to 1497.

With that regard, Portuguese, while waging war against Calicut, simultaneously pursued to establish friendly relations with the rulers of Vijayanagara ( sometimes even offering to Vijayanagara the rest of the Calicut kingdom). It seems that they were relatively successful with at least keeping Vijayanagara uninvolved as Vijayanagara has not taken a side, or any steps in direction of helping Zamorin in this conflicts. With the later Portuguese acquisition of Goa, belonging to Sultanate of Bijapur, enemy of Vijayanagar, the two were drawn closer as both had a common greater enemy (Muslim sultanates of Deccan) rather then bickering over Calicut

TL;DR Calicut was nominally under Vijayanagara Empire. Exact practical relationship at that point in time is slightly unclear, but probably was some form of vassalage. However Vijayanagara doesn't seem to get involved much in Portuguese hostilities with Calicut