In this case it is the verb which has a future meaning and so the tense is unimportant. You can see this by the fact that you can change the sentence to "he is planning to cycle" without changing the meaning at all, and from the fact that "plan" is almost never used with a future tense such as "going to plan" or "will plan". "want" and "would like" are similar.
The Present Simple tense itself (with verbs which don't have a future meaning) only has two future uses:
- Scheduled events, e.g. "The class starts at eight o'clock"
- First conditional, e.g. "If he gets home before me, I'll..."