Phillips scored the winning goal for the Eagles in their Championship play-off final victory over Watford last month but now finds himself out of contract.
He had been on loan from Blackpool and is now considering his options, with Palace set to offer the 39-year-old a new 12-month deal.
Parish has been impressed by Phillips' attitude during his time at the club and feels his experience could be vital as Palace prepare for life back in the top flight.
"He's someone we feel could still do a job in the Premier League, if we can come to some agreement with him and he is happy to be down in the south of England for another year," said Parish.
"Kevin is super professional and we know he wouldn't make a decision to stay if he wasn't going to give his all."