The 18-year-old Manchester United academy product is scheduled to remain with the Championship outfit until January.
The Posh boss told BBC Radio Cambridgeshire: "Hopefully Ryan wants to stay. Ultimately it's up to him."
Tunnicliffe has made seven starts and 11 substitute appearances since arriving at London Road.
"I know he wants to play more games, but I always make the decisions based on what is right for the club," he said.