The Norway international has become a fans' favourite at Selhurst Park since signing from Aalesund in July 2011, winning the club's 2011-12 Player of the Year Award.
He remained a regular during the 2012/13 season but missed their dramatic promotion to the Premier League via the play-offs due to an ankle injury suffered in April.
The 24-year-old is set to enter the final year of his contract in south London and there had been speculation over his long-term future at the club.
West Bromwich Albion, Norwich and Southampton have all been linked with a move for the versatile full-back in recent weeks.
His agent, Jim Solbakken, has confirmed there have been enquires about the player, but insists Parr is happy to stay with the Eagles and talks have already been held over a new deal.
"We have had small discussions over the last half a year or year and it is most likely we will sit down within a couple of months and see where things go," Solbakken told the South London Press. "There is no stress to the situation. Jonathan likes Crystal Palace a lot.
"There have been enquiries - not only from England but elsewhere in Europe - but he has found himself a home at Palace. There has been nothing more than interest from other clubs. I've not had serious discussions with anybody because of his commitment to Palace.
"We'll see what happens in the rest of the transfer window but there is no panic from any side. We'll just take it easy."