The possible punishments are included in a crackdown by authorities on parking in Stanhope Road and Bowl Alley Lane - close to Horncastle Community Primary School and St Lawrence School.
There have been ongoing complaints about inconsiderate parking at the start and finish of the school day.
The problem has been discussed at length at several meetings of Horncastle Town Council.
Police recently held a site meeting with Horncastle’s County Councillor Bill Aron and an officer from the County Council’s Highways department.
As a result, it has been confirmed members of the town’s Neighourhood Policing Team and Enforcement Officers from the County Council will step up patrols in the area.
It can also be revealed police could issue Community Protection Notices against persistent offenders.
The orders are part of legislation to combat anti-social behaviour.
Warnings form the initial part of an order, but if problems continue individuals can be fined up to £2,000 and/or face a ban from Stanhope Road and Bowl Alley Lane at specific times.
PCSO Nigel Wass, a member of the NPT, said the authorities were determined to solve the parking issues.
He told the News: “This has been an ongoing problem, but it does appear to have got worse recently.
“One issue is that some individuals are parking their vehicles and causing an obstruction.
“People who approach them and politely ask them to move their vehicles have been met with bad language, which is unacceptable.
“We will be stepping up patrols in the area and Traffic Enforcement Officers from the County Council have been made aware, and they will be doing the same.”
The officers from the County Council are responsible for enforcing parking regulation by issuing penalty notices.
PSCO Wass confirmed police would also act if vehicles were found to be causing an obstruction or if bad language was used.
He also stressed Community Protection Notices could be issued.
He added: “Individuals have been spoken to before, but if they ignore warnings, we will take further action.”
Residents have complained vehicles are parking across private driveways or even double-parked on narrow side-roads - leading to access issues.
Speaking at last Tuesday’s Town Council meeting, Coun Aron said he supported any efforts to solve the problem,
There have also been calls for more parents to walk their children to school.