868 people have been fined in Sussex for breaching Covid rules since March.
Police say around around 75 per cent of the Fixed Penalty Notices were given to people visiting from outside the county – mainly those attracted to the beaches during the hot summer weather.
But a couple of hefty penalties are being considered for locals who have flouted the rules, putting themselves and others at risk of infection.
Chief Constable of Sussex Police Jo Shiner said: “We have got a couple of investigations ongoing where we may well issue the £10,000 fine to people who have been incredibly irresponsible.”
Anyone breaking the rules risks a £200 fine for the first offence, doubling for further offences up to a maximum of £6,400.
Someone holding, or involved in holding, an illegal gathering of more than 30 people could face a fine of £10,000.
Sussex Police recently received a £644,621 share of the £30m surge funding provided to help forces in England and Wales keep on top of Covid-19 enforcement.
Mrs Bourne was told that plans were being drawn up to use the money to target towns and communities most affected by people who refuse to comply with the restrictions.
Chief Con Shiner, in a meeting with Police and Crime Commissioner Katy Bourne, said crime levels had returned to pre-Covid levels and urged people to follow pandemic restrictions such as wearing a mask and sticking to the rule of six.