To my knowledge there was never any real discussion of Hong Kong being given to Taiwan instead of the PRC. Although it's never really wise to try and prove a negative, there are a few cogent reasons why it's unlikely this was ever seriously considered by the British:

1. The UK, unlike the US and some other Western states, had recognized the PRC as the government of China since the 1950s. Sino-British relations were very rocky for decades, but by the time negotiations for the return of Hong Kong began there was little question as to which government the UK considered party to the original treaties signed with the Qing Dynasty.
2. At the time the negotiations began, Taiwan was still under military rule. Although it had fully transitioned to democracy by the time the handover occurred, the outcome of that transition was still very much uncertain during the key periods when negotiations were occurring (early 1980s). This would likely have diminished any potential preference for the ROC (Republic of China) government over the PRC by both the UK and the people of Hong Kong.
3. Most real consideration by any nation of the ROC as the legitimate Chinese successor state died in 1971 when the UN voted to admit the PRC as the legitimate government of China (and take it's spot on the security council) and to expel the ROC delegation. By the early 1980s no major Western power officially regarded Taiwan as a country in its own right, let alone party to treaties signed with previous Chinese governments.
4. Even had the UK preferred to hand Hong Kong over to the ROC, there was no practical way the they could maintain control. The PRC were already prepared to take Hong Kong by force from the UK if negotiations failed, and the ROC military was in no position to offer a better defense than the UK. The massive disparity in military strength between the PRC and ROC by this time notwithstanding, Hong Kong is immediately adjacent to the Chinese mainland but separated from Taiwan by over 700km of ocean. It is highly unlikely that even with the support of other nations such as the US that the ROC could have held the island of Hong Kong, let alone the mainland portions of the territory.

Without a direct source from the UK side attesting to this question it's impossible to say whether returning Hong Kong to Taiwan was ever brought up, but for many reasons including those outlined above it seems unlikely it could ever have been considered in earnest.