Hot Jupiters (HJ) are defined as Jupiter-mass exoplanets orbiting around their host star with an orbital period < 10 d. It is assumed that HJ do not form in-situ but ex-situ. Recent discoveries show that star clusters contribute to the formation of HJ. We present direct N-body simulations of planetary systems in star clusters and analyse the formation of HJ in them. We combine two direct N-body codes: NBODY6++GPU for the dynamics of dense star clusters with 32 000 and 64 000 stellar members and LONELYPLANETS used to follow 200 identical planetary systems around solar mass stars in those star clusters. We use different sets with three, four, or five planets and with the innermost planet at a semimajor axis of 5 or 1 au and follow them for 100 Myr in our simulations. The results indicate that HJs are generated with high efficiency in dense star clusters if the innermost planet is already close to the host star at a semimajor axis of 1 au. If the innermost planet is initially beyond a semimajor axis of 5 au, the probability of a potential HJ ranges between 1.5 and 4.5 per cent. Very dense stellar neighbourhoods tend to eject planets rather than forming HJs. A correlation between HJ formation and angular momentum deficit is not witnessed. Young HJs (tage < 100 Myr) have only been found, in our simulations, in planetary systems with the innermost planet at a semimajor axis of 1 au.