Parish described Zaha as the 'best player' in the Championship, and the 19-year-old has become one of the most in-demand players leading up to the January transfer window, with Arsenal, Liverpool and City all credited with an interest in the youngster.
Zaha was superb for Palace during this weekend's 2-0 victory over Blackburn, as the south London side moved up to third in the Championship table.
And Parish made it clear he'll be doing everything he can to make sure new boss Ian Holloway has the best possible squad for a promotion push in the New Year.
"If someone came in with £20m to spend then it would be very difficult to turn down - but we might still say no," Parish was quoted on talkSPORT.
"He is our talisman, the best player in the league. My plan for January is to turn my phone off and go into hibernation. Then I wont listen to any offers and we will come out of the month intact."
Arsenal, Liverpool and Manchester City have all been reportedly scouting the Palace star, with a view to possibly making a bid in January.
The England under-21 star is widely regarded to be one of England's brightest prospects, and the teenage winger has earned a reputation as a first-class dribbler with an eye for goal.
Liverpool have given youth a chance this season under Brendan Rodgers, with Raheem Sterling, Suso and Andre Wisdom all promoted to the Reds first-team, while Arsenal have a reputation for giving youngsters a chance, and the Gunners could be tempted to move for Zaha.
Manchester City have also insisted that their focus has now switched from big-money purchases for established stars to a more youth-focused approach.