Separately, up to 10 caravans have set up camp in the Laraghbryan Cemetery car park in Maynooth.
A letter from Kildare County Council to St John Of God, the owners of Abbey Car Park in Celbridge, is expected to be delivered today.
In it, local councillors are requesting a meeting to deal with issues of anti-social behaviour.
A number of incidents have been reported to Gardai, with some locals feeling "intimidated" by the current situation and believe that barriers would help prevent illegal encampments.
Barriers, which were previously in place, were removed and have not been replaced, raising concerns among residents and local businesses.
Local businesses have also expressed their concerns, with representations on their behalf submitted to Kildare County Council.
Kfm understands that locals using the outdoor gym equipment are being chased out of the car park.
There have also been reports of fires being lit in the car park and rubbish being dumped.
Kfm has contacted St John Of God to confirm if representatives will meet with local councillors.
Separately, up to 10 caravans have set up camp in the Laraghbryan Cemetery car park in Maynooth.
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