The winger played for nine different clubs before joining Palace on loan at the start of the season.
His form earned him a permanent move in January, and Pulis is hoping to keep Puncheon at his boyhood club.
"I didn't realise he had had nine clubs," Pulis told reporters. "That's more than in my golf bag.
"He's happy and we just hope and pray he continues this form until the end of the season.
"Punch could be anything he wanted to be. Jason has got the tools to be a top player."
Palace's next game is against Aston Villa tomorrow.